1 Number Series

7/21/2019 1 Number Series

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EBMZCA CODADZT

Ebmtca codadty ds thb codadty ti jdstdmùdsh obtwbbmrd`ht cmj wrim`, ti kuj`b thb edmutbst jdnnbrbmgb cmj

ti cjcpt ti thb bvbr ghcm`dm` bmvdrimebmt, thb wdt

ti ecstbr thb sdtuctdim, thb gcpcgdty ti abcrm cmj ti

put pcst bxpbrdbmgb ti thb eist cjvcmtc`bius usb dm

nuturb cmj thb codadty ti jdstdmùdsh obtwbbm

depirtcmt, abss depirtcmt cmj eirb depirtcmt.

BXCE\ABW Giepabtdm` thb @dvbm Wbrdbs

Bx.3 Phdgh mueobr wiuaj rbpacgb qubstdim ecrf dm

thb sbrdbs 0, 3?, 34, 9, 74.

(C) ?4 (O) ?8

(G) ?> (J) ?:

Wia. Gabcray, thb `dvbm sbqubmgb niaaiws thb pcttbrm;

+2, +0, +4 ... d.b., 0 + 2 5 3?, 3? + 0 5 34, ...

Edssdm` mueobr 5 34 + 4 5 ?8

Hbmgb, thb cmswbr ds (O).

Bx.? Phdgh ds thb mueobr thct giebs mbxt dm thb

sbqubmgb ; <, >, ?:, ><, 3?<, ?3< 9

(C) ?:< (O) ?4< (G) 77> (J) 2<:

Wia. Gabcray, thb `dvbm sbrdbs ds

37 ‗ 3, ?7 ‗ ?, 77 ‗ 7, :7 ‗ :, 27 ‗ 2, >7 ‗ >.

Mbxt mueobr 5 07 ‗ 0 5 7:7 ‗ 0 5 77>

Hbmgb, thb cmswbr ds (G).

Bx.7 Phdgh ds thb mueobr thct giebs mbxt dm thb

niaaiwdm` sbqubmgb 9

:, >, 3?, 3:, ?8, 7<,(...)

(C) 7? (O) >< (G) >? (J) >:

Wia. Zhb `dvbm sbqubmgb ds c gieodmctdim in twi

sbrdbs ;

D. :, 3?, ?8 (...) cmj DD. >, 3:, 7<.

Miw, thb pcttbrm niaaiwbj dm bcgh in thb coivb

twi sbrdbs ds ; +8, +3>, +7? ....

Wi, edssdm` mueobr 5 (?8 + 7?) 5 ><


Bx.: Ndmj iut thb edssdm` mueobr dm thb niaaiwdm`

sbqubmgb ; 3, 7, 7, >, 0, 4, 9, 3?, ?3.

(C) 3< (O) 33 (G) 3? (J) 37

Wia. Gabcray, thb `dvbm sbqubmgb ds c gieodmctdim in

twi sbrdbs ;

D. 3, 7, 0, 9, ?3 cmj DD. 7, >, 4, 3?

Zhb pcttbrm niaaiwbj dm D ds + ?, + :, ...6 cmj thb

pct tbrm nia aiwb j dm DD ds +7. Zhus, edssdm`

mueobr 5 0 + > 5 37.

Hbmgb, thb cmswbr ds (J).Bx.2 Phdgh nrcgtdim giebs mbxt dm thb sbqubmgb

?

3,

:

7,

8

2,

3>

0, 9

(C)7?

4(O)

30

3<(G)

7:

33(J)

72

3?

Jbndmdtdim

Giepabtdm` thb sbrdbs

Crdthebtdg Wbrdbs

Wbrdbs in Guobs, Wqucrbs

Edxbj Wbrdbs

Zwi-ZdbrCrdthbebtdg sbrdbs

Zhrbb-ZdbrCrdthbebtdg sbrdbs

Zwdm-Wbrdbs

Zwi admb mueobr sbrdbs

Prim` Mueobr sbrdbs

MRE _ W _D W 3GHC\ZB_



EBMZCA CODADZT

Wia. Gabcray, thb muebrctirs in thb nrcgtdims dm thb

`dvbm sbqubmgb nire thb sbrdbs 3, 7, 2, 0, dm

whdgh bcgh tbre ds iotcdmbj oy cjjdm` ? ti thb

prbvdius tbre. Zhb jbmiedmctirs in thb nrcgtdims

nire thb sbrdbs ?, :, 8, 3>,

d.b. ?3, ??, ?7, ?:.Wi, thb muebrctir in thb mbxt nrcgtdim wdaa ob

(0 + 3?) d.b., 4 cmj thb jbmiedmctir wdaa ob ?2 d.b. 7?.

Zhb mbxt tbre ds7?

4

Hbmgb, thb cmswbr ds (C).

Babebmtcry Djbc in \ri`rbssdims

(D) Crdthebtdg \ri`rbssdim (C.\.)

Zhb pri`rbssdim in thb nire c, c + j, c + ?j,

c + 7j, ... ds fmiwm cs cm C.\. wdth ndrst tbre 5c cmj gieeim jdnnbrbmgb 5 j.

Bx. 7, >, 4, 3?, .... ds cm C.\. wdth c 5 7 cmj

j 5 > ‗ 7 5 7.

Dm cm C.\., wb hcvb mth tbre 5 c + (m ‗ 3)j.

(DD) @biebtrdg \ri`rbssdim (@.\.)

Zhb pri`rbssdim in thb nire c, cr, cr ?, cr 7, ... ds

fmiwm cs c @.\. wdth ndrst tbre 5 c cmj gieeim

rctdi 5 r.

Bx. 3, 2, ?2, 3?2, ... ds c @.\. wdth c 5 3 cmj

r 532 5

2?2 5 ... 5 2.

Dm c @.\. wb hcvb mth tbre 5 cr m‗3.

BXCE\ABW Bx.> Dm thb sbrdbs 720, 7>7, 7>4, ..., whct wdaa ob thb

3<th tbre 9

(C) :<2 (O) :33 (G) :37 (J) :30

Wia. Zhb `dvbm sbrdbs ds cm C.\. dm whdgh c 5 720 cmj

j 5 >.

3<th tbre 5 c + (3< ‗ 3) j 5 c + 4j.

5 (720 + 4 Ð >) 5 (720 + 2:)

5 :33


Bx.0 Hiw ecmy tbres crb thbrb dm thb sbrdbs ?<3, ?<8,

?32, .... 7>4 9

(C) ?7 (O) ?: (G) ?2 (J) ?>

Wia. Zhb `dvbm sbrdbs dm cm C.\. dm whdgh c 5 ?<3 cmj

j 5 0.

Abt thb mueobr in tbres ob m.

Zhbm, 7>4 5 ?<3 + (m ‗ 3) Ð 0 ir m 5 ?2.


Bx.8 Dm thb sbrdbs 0, 3:, ?8, ..., whct wdaa ob thb 3<th

tbre 9

(C) 304? (O) ?:2> (G) 728: (J) :<4>

Wia. Gabcray, 0 Ð ? 5 3:, 3: Ð ? 5 ?8, ... cmj si im.

Wi, thb `dvbm sbrdbs ds c @.\. dm whdgh

c 5 0 cmj r 5 ?.

3<th tbre 5 cr (3<‗3) 5 cr 4 5 0 Ð ?4

5 0 Ð 23? 5 728:


Bx.4 3, :, 4, 3>, ?2, (...)(C) 72 (O) 7> (G) :8 (J) :4

Wia. Zhb mueobrs crb 3?, ??, 7?, :?, 2?

Edssdm` mueobr 5 >? 5 7>

Bx.3< ?<, 34, 30, (...), 3<, 2

(C) 3? (O) 37 (G) 3: (J) 32

Wia. Zhb pcttbrm ds ‗3, ‗?, ...

Edssdm` mueobr 5 30 ‗ 7 5 3:

Bx.33 ?, 7, 2, 0, 33, (...), 30

(C) 3? (O) 37 (G) 3: (J) 32

Wia. Gabcray, thb `dvbm sbrdbs gimsdsts in prdebmueobrs stcrtdm` nrie ?. Zhb prdeb mueobr

cntbr 33 ds 37. Wi, 37 ds thb edssdm` mueobr.

Bx.3? >, 33, ?3, 7>, 2>, (...)

(C) :? (O) 23 (G) 83 (J) 43

Wia. Zhb pcttbrm ds +2, +3<, +32, + ?<, ...

Edssdm` mueobr 5 2> + ?2 5 83

Bx.37 3, >, 37, ??, 77, (...)

(C) :: (O) :2 (G) :> (J) :0

Wia. Zhb pcttbrm ds + 2, + 0, + 4, + 33, ...

Edssdm` mueobr 5 77 + 37 5 :>

Bx.3: 7, 4, ?0, 83, (...)

(C) 7?: (O) ?:7 (G) ?3< (J) 3>?

Wia. Bcgh tbre in thb `dvbm sbrdbs ds iotcdmbj oy

euatdpaydm` dts prbgbjdm` tbre oy 7.

Edssdm` mueobr 5 83 Ð 7 5 ?:7



EBMZCA CODADZT

Bx.32 3, 4, 30, 77, :4, 07, (...)

(C) 40 (O) 48 (G) 44 (J) 3<<

Wia. Zhb pcttbrm ds +8, +8, +3>, +3>, +?:, ...

Edssdm` mueobr 5 07 + ?: 5 40

Bx.3> ?, 2, 4, (...), ?<, ?0(C) 3: (O) 3> (G) 38 (J) ?:

Wia. Zhb pcttbrm ds +7, +:, ...

Edssdm` mueobr 5 4 + 2 5 3:

Bx.30 2, 4, 30, ?4, :2, (...)

(C) >< (O) >2 (G) >8 (J) 0<

Wia. Zhb pcttbrm ds +:, +8, +3?, +3>, ...

Edssdm` mueobr 5 :2 + ?< 5 >2

Bx.38 7, 0, 32, 73, >7, (...)

(C) 4? (O) 332 (G) 3?0 (J) 373

Wia. Bcgh mueobr dm thb sbrdbs ds thb prbgbjdm`mueobr euatdpadbj oy ? cmj thbm dmgrbcsbj oy 3.

Zhus, (7 Ð ?) + 3 5 0, (0 Ð ?) + 3 5 32,

(32 Ð ?) + 3 5 73 cmj si im.

Edssdm` mueobr 5 (>7 Ð ?) + 3 5 3?0

Bx.34 3, >, 32, (...), :2, >>, 43

(C) ?2 (O) ?> (G) ?0 (J) ?8

Wia. Zhb pcttbrm ds +2, +4, ..., +?3, +?2

Edssdm` mueobr 5 32 + 37 5 ?8

Bx.?< 3, ?, 7, 2, 8, (...)

(C) 4 (O) 33 (G) 37 (J) 32

Wia. Bcg h t bre d m t hb sb rd bs d s t hb su e i n t hb

prbgbjdm` twi tbres.

Zhus, 3 + ? 5 76 ? + 7 5 26 7 + 2 5 8 cmj si im.

Edssdm` mueobr 5 2 + 8 5 37

Wbrdbs

Wbrdbs ds c sbqubmgb in mueobrs iotcdmbj oy

sieb pcrtdguacr prbjbndmbj ruab cmj cppaydm` thct

prbjbndmbj ruab dt ds pissdoab ti ndmj iut thb mbxt

tbre in thb sbrdbs.

C sbrdbs gcm ob grbctbj dm ecmy wcys. Wieb in

thbsb crb jdsgussbj obaiw ;

(d) Crdthebtdg Wbrdbs.

Nir bxcepab,

7, 2, 0, 4, 33,......

3<, 8, >, :, ?,......

37, ??, 73, :<, :4,.....

73, ?0, ?7, 34, 32,.....btg.

crb crdthebtdg sbrdbs obgcusb dm bcgh in thbe thb

mbxt mueobr gcm ob iotcdmbj oy cjjdm` ir

suotrcgtdm` c ndxbj mueobr. Nir bxcepab dm 7, 2,

0, 4, 33,..... bvbry suggbssdvb mueobr ds iotcdmbj

oy cjjdm` ? ti thb prbvdius mueobr.

(dd) @biebtrdg Wbrdbs.

Nir bxcepab,

:, 8, 3>, 7?, >:,....

32, ‗7<, ><, ‗3?<, ?:<,....

3<?:, 23?, ?2>, 3?8, >:,....

73?2, ‗>?2, 3?2, ‗?2, 2,.....

crb `biebtrdg sbrdbs obgcusb, dm bcgh in thbe,

thb mbxt mueobr gcm ob iotcdmbj oy euatdpaydm`

(ir jdvdjdm )̀ thb prbvdius mueobr oy c ndxbj

mueobr. (Nir bxcepab, dm ; 73?2‗>?2, 3?2, ‗?2, 2...bvbry suggbssdvb mueobr ds iotcdmbj oy jdvdjdm`

thb prbvdius mueobr oy ‗2.)

(ddd) Wbrdbs in squcrbs, guobs ;

Zhbsb sbrdbs gcm ob nirebj oy squcrdm` ir guodm`

bvbry suggbssdvb mueobr.

Nir bxcepab,

?, :, 3>, ?2>,.....

7, 4, 83, >2>3,....

?, 8, 23?,.... btg.

crb sugh sbrdbs. (Dm thb ndrst cmj sbgimj, bvbry

mueobr ds squcrbj ti `bt thb mbxt mueobr whdab

dm thb thdrj dt ds guobj).

(dv) Edxbj Wbrdbs ;

Oy c edxbj sbrdbs, wb ebcm c sbrdbs whdgh ds

grbctbj cggirjdm` ti cmy mim-gimvbmtdimca (out

ai`dgca) ruab. Obgcusb thbrb ds mi adedtctdim ti

pbipab's dec`dmctdim, thbrb crb dmndmdtb wcys dm

whdgh c sbrdbs gcm ob grbctbj cmj mcturcaay dt ds

mit pissdoab ti gauo ti`bthbr caa in thbe.

Gacssdndgctdim

(D) Zwi-tdbr Crdthebtdg Wbrdbs ;

Dm cm crdthebtdg sbrdbs thb jdnnbrbmgb in cmy twi

suggbssdvb mueobrs ds ndxbj. C Zwi-tdbr Crdthebtdg

Wbrdbs shcaa ob thb imb dm whdgh thb jdnnbrbmgbs

in suggbssdvb mueobrs thbesbavbs nire cm

crdthebtdg sbrdbs.



EBMZCA CODADZT

Nir bxcepab,

(c) 3, ?, 2, 3<, 30, ?>, 70,.....

(o) 7, 2, 4, 32, ?7, 77, .....btg.

crb bxcepabs in sugh sbrdbs. Dm 3, ?, 2, 3<, 30, ?>,

70, ......6 nir bxcepab, thb jdnnbrbmgbs in suggbssdvb

mueobrs crb 3, 7, 2, 0, 4, 33, ....whdgh ds cm

crdthebtdg sbrdbs.

Mitb ;

Zwi-tdbr crdthebtdg sbrdbs gcm ob jbmitbj cs c

qucjrctdg numgtdim. Nir bxcepab, thb coivb sbrdbs

(c) ds <? + 3, 3? + 3, ?? + 3, 7? + 3,.... whdgh gcm ob

jbmitbj cs n(x) 5 x? + 3, whbrb x 5 <, 3, ?,....

sdedacray bxcepab (o) gcm ob jbmitbj cs

n(x) 5 x? + x + 7, x 5 <, 3, ?, 7,.....

(DD)Zhrbb-tdbr Crdthebtdg Wbrdbs ;

Zhds, cs thb mceb su``bsts, ds c sbrdbs dm whdgh

thb jdnnbrbmgbs in suggbssdvb mueobrs nire c

twi-tdbr crdthebtdg sbrdbs6 whisb suggbssdvb

tbre's jdnnbrbmgbs, dm turm, nire cm crdthebtdg

sbrdbs.

Nir bxcepab

(c) 77>, ?3<, 3?<, ><, ?:, >, <,...

ds cm bxcepab in thrbb-tdbr crdthebtdg sbrdbs.

VZhb jdnnbrbmgbs in suggbssdvb tbres crb 3?>, 4<,

><, 7>, 38, >,.....

Zhb jdnnbrbmgbs in suggbssdvb tbres in thds mbwsbrdbs crb 7>, 7<, ?:, 38, 3?,.....

whdgh ds cm crdthebtdg sbrdbs.U

Mitb ;

Zhrbb-tdbr crdthebtdg sbrdbs gcm ob jbmitbj cs c

guodg numgtdim. Nir bxcepab, thb coivb sbrdbs ds

(nrie rd`ht bmj) 37 ‗3, ?7 ‗?, 77 ‗7, :7 ‗:, ....

whdgh gcm casi ob jbmitbj cs n(x) 5 x7 ‗x6 x 5 3,

?,....

(DDD) Depirtcmt _bsuats

Dm cm crdthebtdg sbrdbs wb cjj (ir jbjugt) c ndxbjmueobr ti ndmj thb mbxt mueobr, cmj

Dm c `biebtrdg sbrdbs wb euatdpay (ir jdvdjb) c

ndxbj mueobr ti ndmj thb mbxt mueobr.

Pb gcm gieodmb thbsb twi djbcs dmti imb ti

nrie

(c) Crdthebtdgi-`biebtrdg Wbrdbs ;

Zhds sbrdbs bcgh suggbssdvb tbre shiuaj ob niumj

oy ndrst cjjdm` c ndxbj mueobr ti thb prbvdius

tbre cmj thbm euatdpaydm` dt oy cmithbr ndxbj

mueobr.

Nir bxcepab

3, >, ?3, >>, ?<3,.........

ds cm crdthebtdgi-`biebtrdg sbrdbs. (Bcgh

suggbssdvb tbre ds iotcdmbj oy ndrst cjjdm` 3 ti

thb prbvdius tbre cmj thbm euatdpaydm` dt oy 7).

Mitb ;

Zhb jdnnbrbmgbs in suggbssdvb mueobrs shiuaj

ob dm @biebtrdg \ri`rbssdim.

Dm thds gcsb, thb suggbssdvb jdnnbrbmgbs crb 2, 32,

:2, 372,.... whdgh crb dm @.\.

(o) @biebtrdgi-Crdthebtdg WbrdbsC `biebtrdgi-crdthebtdg sbrdbs shiuaj ob thb imb

dm whdgh bcgh suggbssdvb tbre ds niumj oy ndrst

euatdpaydm` (ir jdvdjdm`) thb prbvdius tbre oy c

ndxbj mueobr cmj thbm cjjdm` (ir jbjugtdm`)

cmithbr ndxbj mueobr.

Nir bxcepab

7, :, 0, 3>, :7, 3?:,....

d s c ` b ie bt rdg i -c rdt h eb t dg sb rd bs. (Bcg h

suggbssdvb tbre ds iotcdmbj oy ndrst euatdpaydm`

thb prbvdius mueobr oy 7 cmj thbm suotrcgtdm`

2 nrie dt.)Mitb ;

Zhb jdnnbrbmgbs in suggbssdvb mueobrs shiuaj

ob dm `biebtrdg pri`rbssdim. Dm thds gcsb, thb

suggbssdvb jdnnbrbmgbs crb 3, 7, 4, ?0, 83, ....whdgh

crb dm @.\.

(D^) Zwdm Wbrdbs ;

Pb shcaa gcaa thbsb twdm sbrdbs, obgcusb thby crb

twi sbrdbs pcgfbj dm imb.

3, 7, 2, 3, 4, ‗7, 37, ‗33, 30,.......

ds cm bxcepab in twdm sbrdbs. (Zhb ndrst, thdrj, ndnthbtg., tbres crb 3, 2, 4, 37, 30 whdgh ds cm crdthebtdg

sbrdbs. Zhb sbgimj, niurth, sdxth btg. crb 7, 3, ‗

7, ‗33 whdgh ds c `biebtrdgi-crdthebtdg sbrdbs dm

w hd g h su gg b ssd vb t b re s c rb i o tc d mb j o y

euatdpaydm` thb prbvdius tbre oy ? cmj thbm

suotrcgtdm` 2.)



EBMZCA CODADZT

(^) Ithbr Wbrdbs ;

Obsdjbs, muebrius ithbr sbrdbs crb pissdoab cmj

dt ds depissdoab ti bvbm thdmf in caa in thbe.

WREEC_T IN ZH_BB WZB\WV^bry DepirtcmtU

Wtbp D ; Ji c prbadedmcry sgrbbmdm` in thb sbrdbs. Dn dt

ds c sdepab sbrdbs yiu wdaa ob coab ti siavb dt bcsday.

Wtbp DD ; Dn yiu ncda dm prbadedmcry sgrbbmdm` thbm

jbtbredmb thb trbmj in thb sbrdbs. Jbtbredmb whbthbr

dt ds dmgrbcsdm`, jbgrbcsdm` ir catbrmctdm`.

Wtbp DDD (C) ; \brnire thds stbp imay dn c sbrdbs ds

dmgrbcsdm` ir jbgrbcsdm`. Rsb thb niaaiwdm` ruabs ;

(c) Dn thb rdsb in c sbrdbs ds saiw ir `rcjuca, thb sbrdbsd s a d fb a y t i h c vb c m c j jd t di m -o c sb j d mg rbc sb6

suggbssdvb mueobrs crb iotcdmbj oy cjjdm` sieb

mueobrs.

(o) Dn thb rdsb in c sbrdbs ds vbry shcrp dmdtdcaay out

saiws jiwm actbr im, thb sbrdbs ds adfbay ti ob nirebj

oy cjjdm` squcrbj ir guobj mueobrs.

(g) Dn thb rdsb in c sbrdbs ds thriu`hiut bqucaay shcrp,

thb sbrdbs ds adfbay ti ob euatdpadgctdim-ocsbj6

suggbssdvb tbres crb iotcdmbj o y euatdpaydm` oy sieb

tbres (cmj, ecyob, sieb cjjdtdim ir suotrcgtdim giuaj

ob thbrb, tii).

(j) Dn thb rdsb in c sbrdbs ds drrbùacr, thbrb ecy ob

twi pissdodadtdbs. Bdthbr thbrb ecy ob c edx in twi

sbrdbs ir twi jdnnbrbmt fdmjs in ipbrctdims ecy ob

ìdm` im catbrmctbay. (Zhb ndrst ds eirb adfbay whbm

thb dmgrbcsb ds vbry drrbùacr ; thb sbgimj ds eirb

adfbay whbm thbrb ds c pcttbrm, bvbm dm thb drrbùacrdty

in thb sbrdbs).

Wtbp (DDD) (O) ; (ti ob pbrnirebj whbm thb sbrdbs ds

catbrmctdm`)

VWceb cs (dv) in stbp (ddd), Ghbgf twi pissdodadtdbsU

Wieb Wiavbj Bxcepabs

Bx. Ndmj thb mbxt mueobr in thb sbrdbs

(d) 8, 3:, ?>, 2<, 48, 34:

(dd) 8, 8, 4, 4, 33, 3<, 3:, 33

(ddd) 7?2, ?24, ?<:, 3><, 3?0, 3<2

(dv) 2:, :7, 7:, ?0, ??, 34

(v) 8?:, :<8, ?<<, 4>, ::, 38

(vd) 3>, 30, ?3, 7<, :>, 03

(vdd)7, 7, >, 38, 0?, 7><

(vddd) 7, :, 8, 30, 77, 28

(dx) >, 3>, 7>, 0>, 32>, 73>

(x) ‗?, :, ??, 28, 338, ?<8

Wiautdim

(d) Whcrp dmgrbcsb cmj tbres riu`hay jiuoadm` bvbry

tdeb. Im ghbgfdm` wdth ? cs euatdpab thb sbrdbs ds;

mbxt tbre 5 prbvdius tbre Ð ? ‗?. Mbxt tbre 5 78?.

(dd) Drrbùacr. ^bry drrbùacr. Adfbay ti ob, thbrbnirb,

edxbj. Im ghbgfdm` dt ds c edx in twi sbrdbs;

8, 4, 33, 3:, (+3, +?, +7 btg.) cmj 8, 4, 3<, 33.

Mbxt tbre 5 3: + : + 38.

(ddd) @rcjuca saiw jbgrbcsb. Adfbay ti ob crdthebtdgca

jbgrbcsb. Ghbgf thb jdnnbrbmgbs in suggbssdvb

tbres. Zhby crb >>, 22, ::, 77, ??. Hbmgb, mbxt

jbgrbcsb wdaa ob ; 33.

Mbxt tbre 5 3<2 ‗ 33 5 4:.

(dv) @rcjuca saiw jbgrbcsb. Adfbay ti ob crdthebtdgca

jbgrbcsb. Ghbgf thb jdnnbrbmgbs. Zhby crb 33, 4,

0, 2, 7. Hbmgb, mbxt jbgrbcsb wdaa ob 3. Mbxt tbre

5 34 ‗ 3 5 38.

(v) Whcrp jbgrbcsb cmj tbres riu`hay obdm` hcavbjbvbry tdeb. Ghbgfdm` wdth ? cs jdvdsir thb sbrdbs

ds ;

Mbxt tbre (prbvdius tbre ‗ 8) ?.

Mbxt tbre 5 2.

(vd) prbadedmcry sgrbbmdm` tbaas us thct bcgh tbre ds

iotcdmbj oy cjjdm` 3 ?, ??, 7?, :?, 2?......

rbspbgtdvbay.

Mbxt tbre 5 03 + >? 5 3<0

(vdd) Whcrp dmgrbcsb. Zhb sbrdbs ds ; Ð 3, Ð ?, Ð7, Ð:, Ð2,

....Mbxt tbre 5 7>< Ð > 5 ?3><

(vddd) Whcrp dmgrbcsb thct saiws jiwm actbr mi. (_ctdisin suggbssdvb tbres rdsb shcrpay nrie : 7 5 3.7

ti 8 : 5 ? ti 30 8 5 ?. 3?2 cmj thbm stcrt

ncaadm` ti 77 30 3.4 cmj thbm ti 28 77 3.8).

Hbmgb adfbay ti ob cjjdtdim in squcrbj ir guobj

mueobrs. Im ghbgfdm` thb sbrdbs ds;

+ 3? +? ?, +7 ?, +: ?, +2 ?, . .. . M b xt t bre 5

28 + >? 5 4:.



EBMZCA CODADZT

(dx) Whcrp dmgrbcsb wdth tbres riu`hay jiuoadm` bcgh

tdeb. Adfbay ti hcvb `biebtrdgca mcturb wdth ? cs

euatdpab. Im ghbgfdm` thb sbrdbs ds; Ð? +:. Mbxt

tbre 5 73> Ð ? + : 5 >7>

(x) Wbrdbs dmgrbcsbs shcrpay out thbm dts spbbj in

rdsb saiws jiwm. Adfbay ti ob cjjdtdim in squcrbj

ir guobj mueobrs. Im ghbgfdm`, thb sbrdbs ds; 3 7

‗ 7, ?7 ‗ :, 77 ‗ 2, :7 ‗ >.... Mbxt tbre 5 07 ‗ 4

5 77:.

Prim` Mueobr dm Wbrdbs

Dm bxcedmctdims, c sbrdbs ds eirb adfbay ti ob

`dvbm thb nirect in c giepabtb sbrdbs dm whdgh cm

dmgirrbgt mueobr ds dmgaujbj & dt ds rbqudrbj ti

ndmj iut thb wrim` mueobr. Im stujydm` c `dvbm

sbrdbs cmj cppaydm` thb gimgbpts bepaiybj si

ncr yiu shiuaj ob coab ti umjbrstcmj cmj thus"jbgijb" thb nirectdim in thb sbrdbs. Rsucaay sdx

tbres crb `dvbm cmj dt ebcms thct ct abcst ndvb

girrbgt tbres crb `dvbm.

Wieb Rmdqub Wbrdbs

Zhbsb sbrdbs ecy ob csfbj dm bxcedmctdims, si

yiu eust ob cwcrb in thbe.

D. Wbrdbs in Jctb ir Zdeb

3. Phdgh in thb niaaiwdm̀ jibsm't ndt dmti thb sbrdbs9

2‗3‗4>, ?0‗3‗4>, 38‗?‗4>, 3?‗7‗4>,

Wia. Bcgh suggbssdvb jctb jdnnbrs oy ?? jcys. _bgcaa

thct 4> ds c abcp ybcr, yiu wdaa ndmj thct 3?‗7‗4>

shiuaj ob rbpacgbj oy 33‗7‗4>.

?. Phdgh in thb niaaiwdm̀ jibsm't ndt dmti thb sbrdbs9

2.:<, 8.<<, 3<.?<, 3?.7<, 7.<<, 2.?<

Wia. Bcgh suggbssdvb tdeb jdnnbrs oy ? hrs. ?< edmutbs.

Wi 3?.7< shiuaj ob rbpacgbj oy 3?.:<.

Mitb ; Fbbp dm edmj thct thb prioabe in sbrdbs ecy ob

ocsbj im jctbs ir tdebs. Wiebtdebs dt jibsm't

strdfb iur edmj cmj thb qubstdim ds siavbj

wrimày.

DD. Nrcgtdimca sbrdbs

Phdgh in thb niaaiwdm` jibsm't ndt dmti thb sbrdbs9

3.2

:,

32

0,

32

3,

2

3 ,

32

8

Wia. Phbmbvbr yiu ndmj thct eist in thb nrcgtdims

hcvb thb sceb jbmiedmctirs, ghcm`b caa thb

jbmiedmctirs ti thb sceb vcaub. Nir bxcepab, dm

thds qubstdim, thb sbrdbs obgiebs ;

323? ,

320 ,

323 ,

327 ,

328

Miw, dt ds gabcr thct muebrctirs eust jbgrbcsb

suggbssdvbay oy 2. Zhbrbnirb,32

3shiuaj ob

rbpacgbj oy32

?.

?.2

:,

72

?7,

72

38,

72

3?,

72

8,

72

7

Wia. Oy thb coivb ruab dn wb ghcm`b caa thb nrcgtdims

wdth thb sceb jbmiedmctirs, thb sbrdbs ds

72

?8,

72

?7,

72

38,

72

3?,

72

8,

72

7.

Pb sbb thct muebrctirs jbgrbcsb oy 2, thus

72

3?shiuaj ob rbpacgbj oy

72

37.

Miw, wb gimga ujb thc t thb coivb nrcgt di ms

jbgrbcsb suggbssdvbay oy72

2ir

0

3.

7??2

338,

344

3<<,

307

8?,

3:0

>>,

3?3

:>,

42

?8

Wia. Pb sbb thct caa thb jbmiedmctirs jdnnbr, si wb

gcm't usb thb coivb ruab. Dm thds gcsb usucaay, thb

muebrctirs cmj jbmiedmctirs ghcm`b dm c

jbndmdtb pcttbrm. Hbrb, muebrctirs jbgrbcsb

suggbssdvbay oy 38 whbrbcs jbmiedmctirs

jbgrbcsb suggbssdvbay oy ?>. Zhus3:0

>>shiuaj

ob rbpacgbj oy3:0

>:.

:. 84

3?

, 8>

32

, 8?

38

, 8<

?3

, 00

?:

, 0:

?0

Wia. Muebrctirs dmgrbcsb suggbssdvbay oy 7 whbrbcs

jbmiedmctirs jbgrbcsb suggbssdvbay oy 7. Zhus

8?

38shiuaj ob rbpacgbj oy

87

38.



EBMZCA CODADZT

DDD. Wieb mueobrs niaaiwbj oy thbdr AGE ir

HGN

3. 3, ?, 7, >, :, 2, >, ><, 2, >, 0,..... (Ndaa up thb oacmf)

Wia. Zhb sbrdbs gcm ob sbpcrctbj dm thrbb pcrts. 3, ?,

7, >/:, 2, >, ></2, >, 0..... Dm bcgh pcrt niurthmueobr ds AGE in ndrst thrbb

?. 8, >, ?:, 0, 7, ?3, 2, :, ?<,.....,4, 38

(3) 3 (?) 7 (7) : (:) 2 (2) >

Wia. 8, >, ?:/0, 7, ?3/2, :, ?</Y, 4, 38

Zhdrj mueobr dm bcgh pcrt ds AGE in ndrst twi

mueobrs. Zhus, thb cmswbr shiuaj ob >.

7. 8, :, :, 0, 8, 3, 7, 4, 7, ?, 3,....

(3) 3 (?) ? (7) 7 (:) 2 (2) M.I.Z

Wia. 8, :, :/0, 8, 3/7, 4, 7/?, 3...

Dm bcgh pcrt, thdrj mueobr ds HGN in ndrst ti

mueobrs. Zhus iur cmswbr shiuaj ob 3.

D .̂ Wieb mueobrs niaaiwbj oy thbdr prijugt

3. ?, 7, >, 38, 3<8, 38::

Phdgh in thb coivb mueobrs jibs mit ndt dmti

thb sbrdbs9

Wia. 38:: ds wrim`, obgcusb

? Ð 7 5 >, 7 Ð > 5 38, 38 Ð > 5 3<8,

out 3<8 Ð 38 5 34::.

.̂ Oy usb in jd d̀t-sue

3. 3:, 34, ?4, :<, ::, 23, 24, 07

Phdgh in thb coivb mueobrs jibsm't ndt dmti thb

sbrdbs 9

Wia. Mbxt mueobr 5 \rbvdius mueobr + Jd d̀t-sue in

prbvdius mueobr Adfb,

34 5 3: + (: + 3)

?4 5 34 + (3 + 4)

:< 5 ?4 + (? + 4)

Zhus, wb sbb thct 23 shiuaj ob rbpacgbj oy 2?.

?. Ndaa up thb oacmfs

3:, 2, 38, 4, ??, :, ?>, 8, 7<, 7, ....., .....

Wia. 3st, 7rj, 2th, 0th, ... mueobrs niaaiw thb pcttbrm

in +: (3: + : 5 38, 38 + : 5 ??,...). Phbrb cs ?mj,

:th, >th crb thb jd d̀t-sues in thbdr rbspbgtdvb

prbvdius mueobr (2 5 3 + :, 4 5 3 + 8),...) Zhus,

iur cmswbr ds 7: cmj 0.

^D. Ijj mueobr iut

Wiebtdebs c `riup in mueobrs ds wrdttbm iut in

whdgh imb ds jdnnbrbmt nrie ithbrs.

3. ??, ::, 88, 37?, 3>2, 343, ?:?. Ndmj thb mueobr

whdgh jibsm't ndt dm thb coivb sbrdbs (ir `riup).

Wia. 3436 Ithbrs crb jdvdsdoab oy 33 ir 343 ds thb

sdmàb prdeb mueobr.

?. Phdgh imb in thb niaaiwdm` sbrdbs jibsm't ndt dmti

thb sbrdbs 9

?4, 73, 70, :7, :0, 23, 27

Wia. 236 Caa ithbr crb prdeb mueobrs.

Zwi-admb Mueobr Wbrdbs

Miw c jcys thds typb in mueobr sbrdbs ds casi

obdm` csfbj dm bxcedmctdims.

Dm thds typb in mi. sbrdbs imb giepabtb sbrdbs ds

`dvbm whdab thb ithbr ds dmgiepabtb. Oith thb

sbrdbs hcvb thb sceb jbndmdtb ruab. Cppaydm` thb

vbry jbndmdtb ruab in thb giepabtb sbrdbs, yiu

hcvb ti jbtbredmb thb rbqudrbj mi. in thb

dmgiepabtb sbrdbs. Nir bxcepab;

Bx.?3 : 3 : 7 > 3 3: : ><

? c o g j b

Ndmj thb vcaub in b.

Wia. Zhb ndrst sbrdbs ds Ð3 + 3<, Ð? +8, Ð7 +>, Ð: + :,.....

c 5 ? Ð 3 + 3< 5 3?, o 5 3? Ð ? + 8 5 7?,

g 5 7? Ð 7 + > 5 3<?, j 5 3<? Ð : + : 5 :3?,

cmj ndmcaay b 5 :3? Ð 2 + ? 5 ?<>?

Bx.?? 2 > 33 ?8 03 3><

? 7 c o g j b

Phct ds thb vcaub in b9

Wia. Zhb jdnnbrbmgbs in twi suggbssdvb tbres in thb

ndrst sbrdbs crb 3, 2, 30, :7, 84, thb sbqubmgb in

whdgh ds <7 + 3?, 37 + ??, ?7 + 7?, 77 + :?, :7 +

2?.

c 5 7 + 2 5 8, o 5 8 + 30 5 ?2, g 5 ?2 + :7

5 > 8 , j 5 > 8 + 8 4 5 3 2 0 , c m j n d m c a a y

b 5 320 + (27 + >?

5 3?2 + 7> 5) 3>3 5 738



EBMZCA CODADZT

Bx.?7 3?4> 8>: 20> 78: ?2>

3<8< c o g j b

Phct shiuaj rbpacgb g 9

Wia. Zhb ndrst sbrdbs ds 7 Ð ?

c 5 3<8< 7 Ð ? 5 0?<, o 5 0?< 7 Ð ? 5 :8<,cmj ndmcaay g 5 :8< 7 Ð ? 5 7?<

Bx.?: 0 37 08 87 :32

7 c o g j b

Ndmj thb vcaub in o.

Wia. Zhb ndrst sbrdbs ds +>, Ð>, +2, Ð2

c 5 7 + > 5 4 cmj o 5 4 Ð > 5 2:

Bx.?2 7?:< 2:< 3<8 ?0 4

70?< c o g j b

Phct ds thb vcaub in j9

Wia. Zhb ndrst sbrdbs ds >, 2, : , 7

c 5 70?< > 5 >?<, o 5 >?< 2 5 3?:, g 5 3?:

: 5 73, cmj ndmcaay j 5 73 7 5 3<.77

Bx.?> ?0 :: 03 3<8 322

7: c o g j b

Phct ds thb shiuaj rbpacgb b9

Wia. Zhb jdnnbrbmgbs in twi suggbssdvb tbres in thb

sbrdbs crb 30, ?0, 70, :0.

c 5 7: + 30 5 2 3, o 5 2 3 + ? 0 5 08,g 5 08 + 70 5 332, j 5 332 + :0 5 3>?, cmj ndmcaay

b 5 3>? + 20 5 ?34

Bx.?0. 3<8 2? ?: 3< 7

>: c o g j b

Phct ds thb vcaub in g 9

Wia. Zhb sbrdbs ds ‗: ?

c 5 (>: ‗ :) ? 5 7<, o 5(7< ‗ :) ? 5 37,

g 5 (37 ‗ :) ? 5 :.2

Bx.?8 ‗: ‗? ‗3 8 73 ‗3 c o g j b

Ndmj thb vcaub in o.

Wia. Z hb sb rd bs ds r bp bct bj cs Ð? + > c mj

Ð 7 + 0 catbrmctbay.

c 5 ‗3 Ð ? + > 5 : cmj o 5 : Ð 7 + 0 5 34

Bx.?4 2 8 :3 7 7 20 :? >3

7 : c o g j b

Ndmj thb vcaub in j.

Wia. Zhds ds cm catbrmctb mueobr sbrdbs hcvdm` twi

sbrdbs ;W3 5 2 :3 20 >3.

Zhb jdnnbrbmgbs obtwbbm twi suggbssdvb tbres

crb 7> (5 >?), 3> (5 :?), :( 5 ??) cmj

W? 5 8 77 :?

Zhb jdnnbrbmgbs obtwbbm twi suggbssdvb tbres

crb ?2 (5 2?), 4 (5 7?)

o 5 : + ?2 5 ?4 cmj j 5 ?4 + 4 5 78.

Bx.7< Ndmj thb wrim` mueobr dm thb sbrdbs ;

0, ?8, >7, 3?:, ?32, 7:?, 233

(C) 0 (O) ?8 (G) 3?: (J) ?32

Wia. Gabcray, thb girrbgt sbqubmgb ds

?7 ‗ 3, 77 ‗ 3, :7 ‗ 3, 27 ‗ 3, >7 ‗ 3, 07 ‗ 3,

87 ‗3

?8 ds wrim` cmj shiuaj ob rbpacgbj oy

(77 ‗ 3) d.b. ?>.


Bx.73 Ndmj thb wrim` mueobr dm thb sbrdbs ;

7, 8, 32, ?:, 7:, :8, >7

(C) 32 (O) ?: (G) 7: (J) :8

Wia. Zhb jdnnbrbmgb obtwbbm gimsbgutdvb tbres in thb

`dvbm sbrdbs crb rbspbgtdvbay 2, 0, 4, 33 cmj 37.

Gabcray, 7: ds c wrim` mueobr cmj eust ob

rbpacgbj oy (?: + 33) d.b. 72.


Bx.7? ?:, ?0, 73, 77, 7>

(C) ?: (O) ?0 (G) 73 (J) 77

Wia. Bcgh tbre dm thb sbrdbs ds dmgrbcsbj oy 7 ti

iotcdm thb mbxt tbre.

W i, 7 3 d s w ri m` c mj e ust o b rbp ac gb j o y(?0 + 7) d.b. 7<.

Bx.77 34>, 3>4, 3::, 3?3, 8<

(C) 8< (O) 3?3 (G) 3>4 (J) 34>

Wia. Zhb sbqubmgb ds (3:)?, (37)?, (3?)?, (33)?, (3<)?.

Wi, 8< ds wrim` cmj eust ob rbpacgbj oy (3<)? d.b.

3<<.



EBMZCA CODADZT

Bx.7: 7, 2, 0, 4, 33, 37

(C) 7 (O) 2 (G) 0 (J) 4

Wia. Zh b sb rdb s g i m sd sts i n g i m sbg u td v b p rd eb

mueobrs. Wi, 4 ds wrim`.

Bx.72 3?3, 3:7, 3>2, 38>, ?<4(C) 3:7 (O) 3>2 (G) 38> (J) ?<4

Wia. Bcgh tbre in thb sbrdbs ds dmgrbcsbj oy ?? ti

iotcdm thb mbxt tbre.

Wi, 38> ds wrim` cmj eust ob rbpacgbj oy

(3>2 + ??) d.b. 380.

Bx.7> 3, ?, :, 8, 3>, 7?, >:, 4>

(C) : (O) 7? (G) >: (J) 4>

Wia. Bcgh tbre in thb sbrdbs ds iotcdmbj oy euatdpaydm`

thb prbgbjdm` tbre oy ?

W i, 4 > d s w ri m` c mj e ust o b rb pa cg bj o y(>: Ð ?) d.b. 3?8.

Bx.70 8, 3:, ?>, :8, 48, 34:, 78>

(C) 3: (O) :8 (G) 48 (J) 34:

Wia. Bcgh tbre dm thb sbrdbs ds abss thcm twdgb thb

prbgbjdm` tbre oy ?.

Wi, :8 ds wrim` cmj shiuaj ob rbpacgbj oy

(?> Ð ? ‗ ?) d.b. 2<.

Bx.78 8, 37, ?3, 7?, :0, >7, 87

(C) 37 (O) ?3 (G) 7? (J) :0

Wia. Zhb sbqubmgb ds + 2, + 8, +33, ...

: 0 d s w ri m` c mj e ust o b rbp ac gb j o y

(7? + 3:) d.b. :>.

Bx.74 7, 3<, ?0, :, 3>, >:, 2, ?2, 3?2

(C) 7 (O) : (G) 3< (J) ?0

Wia. Zhb girrbgt sbqubmgb ds

7, 7?, 77, :, :?, :7, 2, 2?, 27.Wi, 3< ds wrim` cmj eust ob rbpacgbj oy 7?

d.b. 4.

BXB_GDWB

S.3 7, 32, 72, ...., 44, 3:7.

(C) >7 (O) >4 (G) 00 (J) 83

S.? 2, 33, 30, ...., ?4, :3.

(C) 34 (O) ?3 (G) ?7 (J) ?2

S.7 0, 30, 73, :4 ...., 40, 3?0

(C) 24 (O) >3 (G) 03 (J) 80

S.: 3, 7, >, 3<, 32 ...., ?8, 7>.

(C) ?< (O) ?3 (G) ?7 (J) ?:

S.2 7, >, ?:, 7<, >7, 0?, ....., 37?.

(C) :? (O) 28 (G) 4< (J) 33<

S.> <, ?, 8, 3:, ?:, 7:, ...., >?.

(C) :< (O) :? (G) :8 (J) 2?S.0 :, 4, ?<, 70, ><,....

(C) 88 (O) 84 (G) 4< (J) 43

S.8 >0, 8:, 42, ...., 377, 328.

(C) 33> (O) 3?4 (G) 3<8 (J) 333

S.4 8, 3<, 3:, 38, ...., 7:, 2<, >>

(C) ?8 (O) ?0 (G) ?> (J) ?2

S.3< 3?, ?, ?>, ?, 0:, ?, ...., 32<, 2?, 2?

(C) 72 (O) 374 (G) 0: (J) 3:8

S.33 :, 4, 30, 72, ...., 374.

(C) 84 (O) 04 (G) >4 (J) 24

S.3? 0, 32, 7?, ...., 378, ?83.

(C) 20 (O) >0 (G) 00 (J) 80

S.37 8, 3?, 3<, 3>, 3?, ....

(C) ?< (O) 38 (G) 3> (J) 3:

S.3: 3<, ?, ?<, 7, 7<, :, ....

(C) :< (O) 2< (G) >< (J) 0<

S.32 ?:, >, :8, 3?, 4>, ?: .....

(C) 343 (O) 34? (G) 347 (J) 34:S.3> 7, 3<, 38, ?0, 70, :8, .....

(C) >< (O) 0< (G) 8< (J) 4<

S.30 3, 7, 4, ?0, 83, ?:7, ........

(C) 0?4 (O) 07< (G) 073 (J) 07?

S.38 3<, 0, >, 8, 2, :, ....

(C) : (O) 2 (G) > (J) 0



EBMZCA CODADZT

S.78 :, 3<, (.....), 8?, ?::, 07<

(C) ?: (O) ?8 (G) 00 (J) ?38

S.74 :, 7?, 3?8, (.....)

(C) 3?8 (O) 3:: (G) 34? (J) ?2>

S.:< ?, 2, 4, 34, 70, (.....)(C) 0> (O) 02 (G) 0: (J) 0?

S.:3 ?:, ><, 3?<, ?3<, (.....)

(C) 7<< (O) 77> (G) :?< (J) 2?2

S.:? 3>2, 342, ?22, ?82, 7:2, (.....)

(C) 702 (O) :?< (G) :72 (J) 74<

S.:7 2, 30, 70, >2, (.....), 3:2

(C) 42 (O) 40 (G) 44 (J) 3<3

S.:: 4, 33, ?<, 73, (.....), 8?

(C) :3 (O) 23 (G) >< (J) 03

S.:2 2, 3>, :4, 3<:, (.....)

(C) 332 (O) 3:8 (G) 30< (J) 383

S.:> 7:, 38, 3<, >, :, (.....)

(C) < (O) 3 (G) ? (J) 7

S.:0 :>?, :?<, 78<, (.....), 7<>

(C) 7?? (O) 77? (G) 7:? (J) 72?

S.:8 7, 8, ??, >7, 382, (.....)

(C) 22< (O) 73< (G) ?42 (J) ?82

S.:4 3, ?, 2, 3?, ?0, 28, 3?3, (.....)

(C) ?:> (O) ?:0 (G) ?:8 (J) ?:4S.2< <.2, <.22, <.>2, <.8, (.....)

(C) <.4 (O) <.8? (G) 3 (J) <.42

Jdr bgtdims ;

Dm bcgh in thb niaaiwdm` qubstdims, imb tbre dm thb mueobr

sbrdbs ds wrim`. Ndmj iut thb wrim` tbre.

S.23 78<, 388, 4?, :8, ?<, 8, ?

(C) 388 (O) 4? (G) :8 (J) ?<

S.2? 3, 7, 0, 32, ?0, >7, 3?0

(C) 0 (O) 32 (G) ?0 (J) >7

S.27 2, 3<, 30, ?:, 70

(C) 3< (O) 30 (G) ?: (J) 70

S.2: 3, 7, 3<, ?3, >:, 3?4, ?2>, 008

(C) 3< (O) ?3 (G) 3?4 (J) ?2>

S.22 32, 3>, ??, ?4, :2, 0<

(C) 3> (O) ?? (G) :2 (J) 0<

S.34 2, ?, >, ?, 0, ?, .....

(C) 8 (O) 4 (G) 3< (J) 33

S.?< :, 8, 3>, 7?, >:, 3?8 .....

(C) ?2> (O) ?20 (G) ?28 (J) ?24

S.?3 <.2, 3.2, :.2, 37.2, (.....)(C) :2.2 (O) 74.2 (G) 7<.2 (J) :<.2

S.?? 3?3, ??2, 7>3, (.....)

(C) ::3 (O) :8: (G) 2?4 (J) 0?4

S.?7 <, ?, 8, 3:, (.....), 7:

(C) ?: (O) ?? (G) ?< (J) 38

S.?: 34, ?, 78, 7, 33:, :, (.....)

(C) ??8 (O) ?2> (G) 72? (J) :2>

S.?2 3, ?, 7, >, 4, 38, (.....), 2:

(C) 38 (O) ?0 (G) 7> (J) 83

S.?> :, 2, 4, 38, 7:, (.....)

(C) :7 (O) :4 (G) 2< (J) 24

S.?0 7, >, 38, 0?, (.....)

(C) 3:: (O) ?3> (G) ?88 (J) 7><

S.?8 >>, 7>, 38, (.....)

(C) 7 (O) > (G) 8 (J) 4

S.?4 ?3, ?2, 77, :4, 83, (.....)

(C) 3:2 (O) 3?4 (G) 337 (J) 40

S.7< 3?, 7?, 0?, 32?, (.....)

(C) 73? (O) 7?2 (G) 232 (J) >37

S.73 7, >, 2, ?<, 0, :?, 4, (.....)

(C) 2: (O) >< (G) >> (J) 0?

S.7? 3, 7, :, 8, 32, ?0, (.....)

(C) 70 (O) :: (G) 2< (J) 22

S.77 ?, 32, :3, 8<, (.....)

(C) 333 (O) 3?< (G) 3?3 (J) 37?

S.7: 8, 3<, 3:, 38, (.....), 7:, 2<, >>

(C) ?: (O) ?2 (G) ?> (J) ?0

S.72 3, ?, >, ?:, (.....)(C) >< (O) 42 (G) 3?< (J) 32<

S.7> ?, 7, 8, >7, (.....)

(C) 3<78 (O) 3448 (G) 7<<8 (J) 74>8

S.70 42, 332.2, 378, (.....), 384

(C) 32:.2 (O) 3>?.2 (G) 3>:.2 (J) 3>>.2



EBMZCA CODADZT

S.2> >, 3:, 7<, >:, 3?>

(C) > (O) 3: (G) >: (J) 3?>

S.20 3<, ?>, 0:, ?38, >2:, 34:>, 287:

(C) ?> (O) 0: (G) ?38 (J) >2:

S.28 7, 0, 32, 74, >7, 3?0, ?22, 233(C) 32 (O) 74 (G) >7 (J) 3?0

S.24 ::2, ??3, 3<4, :>, ?2, 33, :

(C) ?2 (O) :> (G) 3<4 (J) ??3

S.>< 3?7>, ?7:>, 7:2>, :2>>, 2>8>

(C) 3?7> (O) 7:2> (G) :2>> (J) 2>8>

S.>3 2, 3<, :<, 8<, 7?<, 22<, ?2><

(C) 8< (O) 7?< (G) 22< (J) ?2><

S.>? 7, ?, 8, 4, 37, ??, 38, 7?, ?7, :?

(C) 8 (O) 4 (G) 37 (J) ??

S.>7 8, ?0, 3?2, 7:7, 3773

(C) 8 (O) 7:7 (G) 3773 (J) Mimb

S.>: 3<, 3:, ?8, 7?, >:, >8, 37?

(C) ?8 (O) 7? (G) >: (J) 37?

S.>2 3, 2, 2, 4, 0, 33, 33, 32, 3?, 30

(C) 33 (O) 3? (G) 30 (J) 32

S.>> 33, ?, ?3, 7, 7?, :, :3, 2, 23, >

(C) ?3 (O) 33 (G) 7? (J) 23

S.>0 33, 2, ?<, 3?, :<, ?>, 0:, 2:

(C) 2 (O) ?< (G) :< (J) ?>S.>8 2>, 0?, 4<, 33<, 37?, 32<

(C) 0? (O) 4< (G) 33< (J) 32<

S.>4 8, 37, ?3, 7?, :0, >7, 87

(C) 37 (O) 7? (G) :0 (J) >7

S.0< 84, 08, 8>, 8<, 82, 8?, 87

(C) 87 (O) 8? (G) 8> (J) 08

S.03 ?2, 7>, :4, 83, 3?3, 3>4, ??2

(C) 7> (O) :4 (G) 3>4 (J) ??2

S.0? ?, 2, 3<, 30, ?>, 70, 2<, >:

(C) 30 (O) ?> (G) 70 (J) >:

Ndmj thb edssdm` mueobr dm thb niaaiwdm` sbrdbs

S.07 :, 0, 33, 38, ?4, :0, ....., 3?7, 344

(C) 0> (O) 0< (G) 8: (J) 3<?

S.0: ?, >, 3?, ?<, ........, :?, 2>, 0?, 4<

(C) ?< (O) ?3 (G) 7< (J) 3?

S.02 30, 0, ?:, 34, 4, ?8, ...., 8, 73, ?0, 3<, 70

(C) ?< (O) ?3 (G) 38 (J) ?7

S.0> >, 3?>,........, 4, 3<8, 3?, 0, 377, 34, 3?, 0?, >

(C) ?3 (O) ?7 (G) 7< (J) 72

S.00 ?, ...........8, 3>, 7?, >:, 3?8, ?2>(C) ? (O) 7 (G) : (J) 2

S.08 :2, 2:, :0,......, :4, 2>, 23, 20, 27

(C) :8 (O) 22 (G) 2< (J) 27

S.04 7, 3?8, >, >:, 4, ....., 3?, 3>, 32, 8

(C) 7? (O) 3? (G) 3<8 (J) 0?

S.8< 2, 0, 33, 34, 72, >0, ...., ?24

(C) >: (O) 373 (G) 372 (J) 7?

S.83 8, :, 3?, >, 38,......?0

(C) 4 (O) 3? (G) 38 (J) ?:

S.8? 3>, ??, 7:, 28, 3<>, ....., 74:

(C) 308 (O) 302 (G) ?88 (J) ?<?

S.87 ?, 7, 2, 4, 30, 77,......

(C) 82 (O) 70 (G) >7 (J) >2

S.8: ?, 4, ?7, 7, 8, ?2, :, ......, ?0

(C) 0 (O) ?4 (G) ?7 (J) 3:

S.82 3?3, 33?, ........, 40, 43, 8>

(C) 3<? (O) 3<8 (G) 44 (J) 3<:

S.8> >, 4, 32, ?0,.....,44

(C) 23 (O) 7: (G) 70 (J) 8:

S.80 :, 0, 3?,......, ?8, 74

(C) 34 (O) ?: (G) 3: (J) 3>

S.88 87, 8?, 83, ....., >4, ><, 77

(C) 07 (O) 8< (G) 02 (J) 00

S.84 00, 08, 00, 83, 07, ...., 22

(C) >4 (O) 03 (G) 8? (J) 84

S.4< >, 0, 4, 37, ?3,......

(C) ?2 (O) ?4 (G) 70 (J) 7?

S.43 2, 0, ......, 4, 0, 33, 8, 37(C) 8 (O) > (G) 34 (J) 0

S.4? :, 8, 3?, ?:, 7>, 0?,......

(C) 3<8 (O) 48 (G) 4? (J) 4>

S.47 3, ?, 7, 2, 0,.....

(C) 8 (O) 4 (G) 3< (J) 37



EBMZCA CODADZT

S.4: 7, >, >, 3?, 4,...........3?

(C) 32 (O) 38 (G) 33 (J) 37

Jd rbgtdims (42 ‗ 3<7) ;

Dm bcgh in thb niaaiwdm` qubstdims, imb mueobr ds wrim`

dm thb sbrdbs. Ndmj iut thb wrim` mueobr ;S.42 7, 2, 3?, 74, 32:, 00?, :>7:

(C) 2 (O) 7 (G) 74 (J) 32:

(B) mimb in thbsb

S.4> 70>, 388, 88, :<, 3>, :, ‗?

(C) : (O) 3> (G) :< (J) 388

(B) mimb in thbsb

S.40 :::, 7<<, ?<<, 37>, 80, 8:, 8<

(C) ?<< (O) 37> (G) 80 (J) 8<

(B) mimb in thbsb

S.48 ?, 7, 3?, 70, 8>, 3>>, ?88

(C) ? (O) 7 (G) 3>> (J) 8>

(B) 70

S.44 :, 4, 34, :7, 4<, 382, 702

(C) 4 (O) 34 (G)4< (J) 382

(B) mimb in thbsb

S.3<< 20?, ?8:, 3:<, 0?, 7?, 3:, 2

(C) 3: (O) 7? (G) 0? (J) 2

(B) 3:<

S.3<3 :, 3<, ?7, 2<, 3<:, ?3>, :74

(C) : (O) 3< (G) ?7 (J) 3<:

(B) ?3>

S.3<? 0<3, 7:8, 307, 82, :3, 34, 8

(C) 307 (O) :3 (G) 34 (J) 8

(B) 7:8

S.3<7 ?, 7, 4, ?0, 33?, 2>2, 774>

(C) 2>2 (O) 4 (G) 33? (J) ?0

(B) 774>

Jdrbgtdim ;

Dm thb niaaiwdm` mueobr sbrdbs, imb in thb mueobrs jibs

mit ndt dmti thb sbrdbs. Ndmj thb wrim` mueobr.

S.3<: 3088, 84?, :::, ??<, 33?, 2?, ?:

(C) 2? (O) 33? (G) ??< (J) :::

(B) 84?

S.3<2 ??2, ?84, 748, 70:, 740, :32, :?:

(C) :32 (O) ?84 (G) 778 (J) 70:

(B) 740

S.3<> 2, 0.2, 33.?2, 30.2, ?4.02, 2<, 43.?2

(C) 0.2 (O) 30.2 (G) ?4.02 (J) 43.?2

(B) Mimb in thbsb

S.3<0 72, 338, ?8<, ><<, 3?78, ?2<:, 2<7>

(C) 338 (O) ?8< (G) ><< (J) 3?78

(B) ?2<:

S.3<8 3<, 3?, ?8, 4<, 7>8, 38:<, 3333?

(C) 38:< (O) 7>8 (G) 4< (J) ?8

(B) 3?

Jdrbgtdims ;

Dm bcgh in thb niaaiwdm` imb mueobr ds wrim` dm thb sbrdbs.

Ndmj iut thb wrim` mueobr dm bcgh gcsb

S.3<4 3, ?, 2, 3:, :3, 3?:

(C) ? (O) 2 (G) 3: (J) :3

(B) 3?:

S.33< 3<<, 40, 4<, 8>, 0>, 03, >?, 22

(C) 22 (O) >? (G) 0> (J) 8>

(B) 40

S.333 3, ?, >, ?:, 3?<, >?<, 2<:<

(C) 2<:< (O) >?< (G) 3?< (J) ?:

(B) >

S.33? :, 3<, ??, :<, >:, 8:, 37<

(C) ?? (O) :< (G) >: (J) 8:

(B) 37<

S.337 3, :, 8, 3>, 73, >:, 3?0, ?2>

(C) 73 (O) 3> (G) 8 (J) >

(B) 3

S.33: :4, 2>, >:, 03, 83, 4<, 3<<, 33<

(C) 2> (O) >: (G) 03 (J) 83

(B) 4<

Jdrbgtdims (332- 334) ;

Dm bcgh qubstdims `dvbm obaiw, Niur iut in thb ndvb `dvbm

sbts in mueobrs niaaiw thb sceb pcttbrm, whdab thb ndnth

imb ds jdnnbrbmt. Tiu hcvb ti ndmj iut thb sbt thct jibs

mit ectgh wdth ithbrs.

S.332 (C) 7 (28) 0 (O) 3 (3<) 7

(G) ? (?<) : (J) 2 (23) >

(B) 8(3:2) 4

S.33> (C) :(7>)? (O) 3<(3<?)3

(G) > (3?3)2 (J) 7(:4) :

(B) 0(??2) 8



EBMZCA CODADZT

S.330 (C) 8(74)2 (O) 3?(::)3<

(G) 0(:8) 3 (J) 4(:2)>

(B) 2(30)?

S.338 (C) 2(>8)4 (O) 33(8)37

(G) 7(?0)> (J) 0(3?2)3?

(B) >(>:)3<

Jdrbgtdims (334- 3?8) ;

Dm bcgh in thb niaaiwdm` qubstdims, c mueobr sbrdbs ds

`dvbm. Cntbr thb sbrdbs , obaiw dt dm thb mbxt admb, c mueobr

ds `dvbm niaaiwbj oy (C), (O), (G), (J) cmj (B). Tiu hcvb

ti giepabtb thb sbrdbs stcrtdm` wdth thb mueobr `dvbm

niaaiwdm` sbqubmgb in thb `dvbm sbrdbs. Zhbm, cmswbr thb

qubstdims `dvbm obaiw dt.

S.334 272, 7>>, ?:2, 3>:,

830 , (c), (o), (g), (j), (b)

Phdgh in thb niaaiwdm` mueobrs wdaa gieb dm pacgb in (b) 9

(C) >:8 (O) 2<0 (G) 780 (J) 70?

(B) mimb in thbsb

S.3?< 7, 2, 38, 0?,

0 , (c), (o), (g), (j), (b)

Phdgh in thb niaaiwdm` mueobrs wdaa gieb dm

pacgb in (j) 9

(C) :3> (O) 4 (G) ?3<< (J) 4>

(B) mimb in thbsb

S.3?3 ?, 4, 20, 770,

7, (c), (o), (g), (j), (b)


pacgb in (o) 9

(C) 337 (O) 30 (G) 743? (J) 8<>2

(B) mimb in thbsb

S.3?? 32, 324, ?24, 7?7,

0, (c), (o), (g), (j), (b)


pacgb in (g) 9

(C) ?23 (O) 732 (G) 30> (J) 323

(B) mimb in thbsb

S.3?7 ?88, 3:<, >>, ?4,

:88, (c), (o), (g), (j), (b)


pacgb in (b) 9

(C) 3<> (O) 38.2 (G) :4 (J) >.?2

(B) mimb in thbsb

S.3?: 3:<, >8, 7>, 3>, 3< 7

?8:, (c), (o), (g), (j), (b)


pacgb in (o) 9

(C) 78 (O) 0? (G) 8: (J) 43

(B) mimb in thbsb

S.3?2 ?2, 34:, 07, 32:, 3<2

3:, (c), (o), (g), (j), (b)


pacgb in (j) 9(C) 4< (O) 8: (G) 3<? (J) 4:

(B) mimb in thbsb

S.3?> >, 4, 38, :2, 372

?<, (c), (o), (g), (j), (b)


pacgb in (g) 9

(C) 7?: (O) 83 (G) 302 (J) 32<

(B) ?3>

S.3?0 ? 4 20 770 3>83

7 (c), (o), (g), (j), (b)


pacgb in (b) 9

(C) 7?:3> (O) :?73 (G) 37::3 (J) >74?

(B) mimb in thbsb

S.3?8 7, :, 3<, 77, 37>

0, (c), (o), (g), (j), (b)


pacgb in (b) 9

(C) 3<72 (O) 33>2 (G) 3<74 (J) 843

(B) mimb in thbsb



EBMZCA CODADZT

HDMZW & WIARZDIM

S.Mi 3 ? 7 : 2 > 0 8 4 3 < 3 3 3 ? 3 7 3 : 3 2 3 > 3 0 3 8 3 4 ? <

Cms. C G G O G G O C G J G O C C O C C G C C

S.Mi ? 3 ? ? ? 7 ? : ? 2 ? > ? 0 ? 8 ? 4 7 < 7 3 7 ? 7 7 7 : 7 2 7 > 7 0 7 8 7 4 : <

Cms. J G C J O J J G C C J G J G G J O O J O

S.Mi : 3 : ? : 7 : : : 2 : > : 0 : 8 : 4 2 < 2 3 2 ? 2 7 2 : 2 2 2 > 2 0 2 8 2 4 > <

Cms. O G J O J J G C G G G G G J O G J O O J

S.Mi > 3 > ? > 7 > : > 2 > > > 0 > 8 > 4 0 < 0 3 0 ? 0 7 0 : 0 2 0 > 0 0 0 8 0 4 8 <

Cms. G O J J O G G J G G C J C G J C G O C O

S.Mi 8 3 8 ? 8 7 8 : 8 2 8 > 8 0 8 8 8 4 4 < 4 3 4 ? 4 7 4 : 4 2 4 > 4 0 4 8 4 4 3 < <

Cms. C J J C J C C J G G O J G O G J G G O G

S.Mi 3 < 3 3 < ? 3 < 7 3 < : 3 <2 3 < > 3 <0 3 < 8 3 < 4 3 3 < 3 3 3 3 3 ? 3 3 7 3 3 : 3 3 2 3 3> 3 3 0 3 3 8 3 3 4 3 ? <

Cms. J B O O B G J C B C O J G G J O B C J C

S.Mi 3 ?3 3 ? ? 3 ? 7 3 ? : 3 ? 2 3 ? > 3 ? 0 3 ?8Cms. C O J O J J G O

3. ?? ‗ 3, :? ‗ 3, >? ‗ 3

?. +>, +>, +> ...

7. +3<, +3:, ...

33. : Ð ? + 3, 4 Ð ? ‗ 3, ...

3:. 3< Ð ? 5 ?<, 3< Ð 7 5 7< ....

?3. Bcgh tbre in thb sbrdbs ds iotcdmbj oy euatdpaydm`

thb prbgbjdm` tbre oy 7.

Edssdm` mueobr 5 37. 2 Ð 7 5 :<.2.

??. Zhb mueobrs crb 33?, 32 ?, 34 ?, . .. d .b. 33?

(33 + : Ð 3)?, (33 + : Ð ?)?, ...

Edssdm` mueobr 5 (33 + : Ð 7)?

5 (?7)? 5 2?4.

?7. Zhb mueobrs crb

3? ‗ 3, ?? ‗ ?, 7? ‗ 3, :? ‗ ?....

Edssdm` mueobr 5 2? ‗ 3 5 ?:.

?:. Zhb sbqubmgb ds c gieodmctdim in twi sbrdbs;

D. 34, 78, 33:, (...) cmj DD. ?, 7, :

Zhb pcttbrm niaaiwbj dm D ds Ð?, Ð7, ...

Edssdm` mueobr 5 3:: Ð : 5 :2>.

?2. Zhb mueobrs crb catbrmctbay euatdpadbj oy ? cmj

?

7. Zhus, 3 Ð ? 5 ?, ? Ð

?

75 7 , 7 Ð ? 5 > ,

> Ð?

75 4 cmj si im.

Edssdm` mueobr 5 38 Ð?

75 ?0.

?>. Z hb p c tt br m d s + 3, + : , + 4 , + 3 >, .. . d .b .,

+ 3?, + ??, + 7?, :?, ....

Edssdm` mueobr 5 7: + 2? 5 7: + ?2 5 24.

?0. Zhb pcttbrm ds Ð?, Ð7, Ð:, ...

Edssdm` mueobr 5 0? Ð 2 5 7><.

?8. Bcgh mueobr dm thb sbrdbs ds thb prijugt in thbjd`dts in thb prbgbjdm` mueobr.

Zhus, > Ð > 5 7>, 7 Ð > 5 38 cmj si im.

Edssdm` mueobr 5 3 Ð 8 5 8.

?4. Zhb pcttbrm ds +:, +8, +3>, +7?, ... d.b., + ??, + ?7,

+ ?:, + ?2,...

Edssdm` mueobr 5 83 + ?> 5 83 + >: 53:2.

7<. Zhb pcttbrm ds +?<, +:<, +8<,...

Edssdm` mueobr 5 32? + 3>< 5 73?.

73. Zhb sbqubmgb ds c gieodmctdim in twi sbrdbs;

, 7, 2, 0, 4 cmj . >, ?<, :?, (.....)Zhb pcttbrm niaaiwbj dm ds + 3:, + ??,...

Edssdm` mueobr 5 :? + 7< 5 0?.

7?. Zhb sue in cmy thrbb gimsbgutdvb tbres in thb

sbrdbs `dvbs thb mbxt tbre. Zhus,

3 + 7 + : 5 86 7 + : + 8 5 326 : + 8 + 32 5?0 cmj

si im.

Edssdm` mueobr 5 8 + 32 + ?0 5 2<.

CMWPB_ FBT



EBMZCA CODADZT

77. Zhb pcttbrm ds + 37, + ?>, + 74, ...

Edssdm` mueobr 5 8< + 2? 5 37?.

7:. Zhb pcttbrm ds + ?, + :, + :, ... 3>, + 3>.

Edssdm` mueobr 5 38 + 8 5 ?>.

72. Zhb pcttbrm ds Ð?, Ð7, Ð:, ....

Edssdm` mueobr 5 ?: Ð 2 5 3?<.

7>. Bcgh tbre dm thb sbrdbs ds imb abss thcm thb squcrb

in thb prbgbjdm` tbre.

Zhus, ?? ‗3 5 7, 7? ‗ 3 5 8, 8? ‗ 3 5 >7.

Edssdm` mueobr 5 (>7)? ‗35 74>4 ‗35 74>8.

70. Zhb pcttbrm ds + ?<.2, + ??.2, ...

Edssdm` mueobr 5 378 + ?:.2 5 3>?.2.

78. Bcgh mueobr dm thb sbrdbs ds thb prbgbjdm`

mueobr euatdpadbj oy 7 cmj thbm jbgrbcsbj oy ?.

74. Zhb pcttbrm ds Ð8, Ð:, ...

Edssdm` mueobr 5 3?8 Ð ? 5 ?2>.

:<. Zhb pcttbrm ds

Ð ? + 3, Ð ? ‗ 3, Ð ? + 3, Ð ? ‗ 3, ...

Edssdm` mueobr 5 70 Ð ? + 3 5 02.

:3. Zhb pcttbrm ds + 7>, + ><, + 4<,... d.b.

+V> Ð(> + <)U,+ V>Ð (> + :)U, + V> Ð(> + 4)U,....

Edssdm` mueobr 5 ?3< + V> Ð (> + 32)U

5 ?3< + 3?> 5 77>.

:?. Bcgh mueobr ds 32 euatdpadbj oy c prdeb mueobr

d.b. 32 Ð 33, 32 Ð 37 , 32 Ð 30, 32 Ð 34, 32 Ð ?7.

Edssdm` mueobr 5 32 Ð ?4 5 :72.

:7. Zhb mueobrs crb ?? + 3 , :? + 3 , >? + 3,

8? + 3, ....3?? + 3.

Edssdm` mueobr 5 3<? + 3 5 3<3.

::. Bcg h t bre dm t h b sbrdb s d s t hb su e in t hb

prbgbjdm` twi tbres.

Edssdm` mueobr 5 ?< + 73 5 23.

:2. Z hb p ct tb rm d s + 3 3 , + 7 7, + 2 2 , . .. d .b .

+ (33 Ð 3), + (33 Ð 7), + (33 Ð 2),...

Edssdm` mueobr 5 3<: + (33 Ð 0) 5 383.

:>. Bcgh tbre ds jdvdjbj oy ? cmj thbm dmgrbcsbj oy

3 ti iotcdm thb mbxt tbre.

Edssdm` tbre 5 (: ?) + 3 5 7.

:0. Zhb pcttbrm ds ‗:?, ‗:<, ...

Edssdm` mueobr 5 78< ‗ 78 5 7:?.

:8. Zhb pcttbrm ds Ð 7 ‗ 3, Ð 7 ‗ ?, Ð 7 ‗ 7, Ð 7 ‗ :,...

Edssdm` mueobr 5 (382 Ð 7) ‗ 2 5 22<.

:4. Z hb p cttbr m ds Ð ? + <, Ð ? + 3 , Ð ? + ? ,Ð ? + 7, Ð ? + :, Ð ? + 2,...

Edssdm` mueobr 5 3?3 Ð ? + > 5 ?:8.

2<. Zhb pcttbrm ds + <.<2, <.3<, + <.32,...

Edssdm` mueobr 5 <.8 + <.?< 5 3.

23. Bcgh tbre dm thb sbrdbs ds niur eirb thcm twi

tdebs thb mbxt tbre. Wi, :8 ds wrim` cmj eust ob

rbpacgbj oy (?< Ð ? + :) d.b.::.

2?. Zhb sbqubmgb ds +?, +:, +8,... d.b. +?, + ??, ?7,...

Wi ?0 ds wrim` cmj eust ob rbpacgbj oy (32 + ?:)

d.b. (32 + 3>) ir 73.

27. Zhb sbqubmgb ds +2, +0,...

Wi, ?: ds wrim` cmj shiuaj ob rbpacgbj oy

(30 + 4) d.b. ?>.

2:. Zhb sbqubmgb ds Ð ? + 3, Ð 7 + 3, Ð ? + 3, Ð 7 + 3,...

Wi, ?2> ds wrim` cmj eust ob rbpacgbj oy

(3?4 Ð ? + 3) d.b. ?24.

22. Zhb pcttbrm ds +3, +:, +4, +3>, +?2, ... d.b. +3?, +

?? + 7?, + :?, + 2?,...

W i, ? ? d s w ri m` c mj e ust o b rbp ac gb j o y

(3> + :) d.b. ?<.

2>. Bcgh tbre ds euatdpadbj oy ? cmj thbm dmgrbcsbj

oy ? ti iotcdm thb mbxt tbre. Wi >: ds wrim` cmj

eust ob rbpacgbj oy (7< Ð ? + ?) d.b. >?.

20. Bcgh tbre ds : abss thcm thrdgb thb prbgbjdm`

mueobr. Wi, >2: ds wrim` cmj eust ob rbpacgbj

oy (?38 Ð 7 ‗ :) 5 >2<.

28. Bcgh mueobr dm thb sbrdbs ds euatdpadbj oy ? cmj

thb rbsuat dmgrbcsbj oy 3 ti iotcdm thb mbxt

mueobr.

Wi, 74 ds wrim` cmj shiuaj ob rbpacgbj oy(32 Ð ? + 3) d.b. 73.

24. 7 ds suotrcgtbj nrie bcgh mueobr cmj thb rbsuat

ds jdvdjbj oy ? ti iotcdm thb mbxt mueobr in thb

sbrdbs.

Wi, :> ds wrim` cmj eust ob rbpacgbj oy?

73<4

d.b. 27.



EBMZCA CODADZT

><. Zhb ndrst jd`dts in thb mueobrs nire thb sbrdbs 3,

?, 7, :, 26 thb sbgimj jd`dts nire thb sbrdbs ?, 7,

:, 2, >6 thb thdrj jd`dts nire thb sbrdbs 7, :, 2, >6

whdab thb acst jd`dt dm bcgh in thb mueobrs ds >.

Wi, 2>8> ds wrim` cmj eust ob rbpacgb oy 2>0>.

>3. Zhb sbqubmgb ds Ð ?, Ð :, Ð ?, Ð :,...

Wi, 22< ds wrim` cmj eust ob rbpacgbj oy

(7?< Ð ?) d.b. >:<.

>?. Zhb `dvbm sbqubmgb ds c gieodmctdim in twi

sbrdbs ;

D. 7, 8, 37, 38, ?7 cmj DD. ?, 4, ??, 7?, :?

Zhb pcttbrm dm ds +2, cmj thb pcttbrm dm DD ds +3<.

Wi, dm , 4 ds wrim` cmj eust ob rbpacgbj oy

(? + 3<) d.b., 3?.

>7. Zhb mueobrs crb guobs in prdeb mueobrs d.b. ?7,

77, 27, 07, 337. Gabcray, mimb ds wrim`.

>:. Catbrmctbay, thb mueobrs crb dmgrbcsbj oy niur

cmj jiuoabj ti `bt thb mbxt mueobr. Wi, 37? ds

wrim` cmj eust ob rbpacgbj oy (>8 Ð ?) d.b. 37>.

>2. Zhb `dvbm sbqubmgb ds c gieodmctdim in twi

sbrdbs ;

D. 3, 2, 0, 33, 3? cmj DD. 2, 4, 33, 32, 30

Zhb pcttbrm dm oith D cmj DD ds +:, +?, +:, +?.

W i, 3 ? d s wrim ` c m j e ust o b rbp ac gb j o y

(33 + ?) d.b., 37.

>>. Zhb `dvbm sbqubmgb ds c gieodmctdim in twi

sbrdbs ;

D. 33,?3, 7?, :3, 23 cmj DD ?, 7, :, 2, >.

Gabcray, thb pcttbrm dm D ds + 3<.

Wi, 7? ds wrim` cmj shiuaj ob rbpacgbj oy

(?3 + 3<) d.b. 73.

>0. Zhb `dvbm sbqubmgb ds c gieodmctdim in twi

sbrdbs ;

D. 33, ?<, :<, 0: cmj DD 2, 3?, ?>, 2:.

Zhb pcttbrm obgiebs +4, + 38, + 7>,... dn :< ds

rbpacgbj oy 78.

Wi, :< ds wrim`.

>8. Z hb m ueo br s cr b 0 Ð 8 , 8 Ð 4 , 4 Ð 3 <,

3< Ð 33, 33 Ð 3?, 3? Ð 37.

Wi, 32< ds wrim` cmj eust ob rbpacgbj oy

(3? Ð 37) d.b. 32>.

>4. Zhb sbqubmgb ds +2, +8, +33, ...

W i, : 0 d s w ri m` c mj e ust o b rbp ac gb j o y

(7? + 3:) d.b., :>.

0<. Zhb sbqubmgb ds ‗33, +4, ‗0, +2, ‗7, +3.

W i, 8 > d s w ri m` c mj e ust o b rbp ac gb j o y(08 + 4) d.b., 80.

03. Zhb girrbgt sbqubmgb ds 2?, 0?, 4?, 33?, 37?, 32?.

Wi, 7> ds wrim`.

0?. Zhb mueobrs crb 3? + 3, ?? + 3, 7? + 3 cmj si

im.

Wi, >: ds wrim`. Zhb girrbgt tbre ds (8? + 3) d.b.

>2.

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