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Hocmai.vnWebsite hc trc tuyn s 1 ti Vit NamKho hc Ton 11 - Thy Nguyn Thanh Tng

Chuyn 03.Dy s, cp s cng v cp s nhn

Hocmai.vnNgi trng chung ca hc tr Vit Tng i t vn: 1900 58-58-12 - Trang | 1 -

I. Phng php quy np ton hc(Ni dung)

Cc bc chng minh mnh ton hc theo phng php quy np ton hc

Bc 1 : Kim tra mnh vi n nh nht ( thng thng n =1 )

Bc 2 : Gi s mnh ng vi n = k

Bc 3 : Chng minh mnh ng vi n = k +1II . Mt s v d

VD1: Chng minh rng :( 1)

1 2 3 ...2

n nn

(n>=1) (1)

Bi lm :

+ Vi n = 1 th 1= 1 ( lun ng )

+ Gi s mnh (1) ng vi n = k, ngha l :

( 1)

1 2 3 ... 2

k k

k

(*)

+ Cn chng minh mnh (1) ng vi n = k+1, ngha l cn chng minh

( 1)( 2)1 2 3 ... ( 1)

2

k kk k

(**)

Tht vy

( 1) 2( 1)1 2 3 ... ( 1) 1

2 2

k kk kk k k

=>(pcm)

VD2: Chng minh rng : ( 1)( 2)1.2 2.3 3.4 ... ( 1)3

n n nn n (2)

+ Vi n = 1 th 1.2= 2 ( lun ng )

+ Gi s mnh (2) ng vi n = k, ngha l :

( 1)( 2)1.2 2.3 3.4 ... ( 1)

3

k k kk k

(*)

+ Cn chng minh mnh (2) ng vi n = k+1, ngha l cn chng minh

( 1)( 2)( 3)

1.2 2.3 3.4 ... ( 1) ( 1)( 2) 3

k k kk k k k

(**)

Tht vy

BI 1. PHNG PHP QUY NP TON HC(PHN 1)

TI LIU BI GING

Gio vin: NGUYN THANH TNGy l ti liu tm lc cc kin thc i km vi bi gingBi 1. Phng php quy np ton hc(phn 1)thuc kha

hcTon 11Thy Nguyn Thanh Tng ti website Hocmai.vn. c th nm vng kin thc. Bn cn kt hp xemti liu cng vibi ging ny.

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Hocmai.vnWebsite hc trc tuyn s 1 ti Vit NamKho hc Ton 11 - Thy Nguyn Thanh Tng

Chuyn 03.Dy s, cp s cng v cp s nhn

Hocmai.vnNgi trng chung ca hc tr Vit Tng i t vn: 1900 58-58-12 - Trang | 2 -

( 1)( 2) ( 1)( 2)( 3)1.2 2.3 3.4 ... ( 1) ( 1)( 2) ( 1)( 2)

3 3

k k k k k k k k k k k k

VD3: Chng minh rng :2

2 2 2 2 (4 1)1 3 5 ... (2 1)

3

n nn

(3)

+ Vi n = 1 th 1= 1 ( lun ng )

+ Gi s mnh (3) ng vi n = k, ngha l :

22 2 2 2 (4 1)1 3 5 ... (2 1)

3

k kk

(*)

+ Cn chng minh mnh (2) ng vi n = k+1, ngha l cn chng minh

22 2 2 2 2 ( 1)(4 8 3)1 3 5 ... (2 1) (2 1)

3

k k kk k

(**)

Tht vy

....................................

Gio vin :Nguyn Thanh Tng

Ngun : Hocmai.vn

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Hocmai.vnWebsite hc trc tuyn s1 ti Vit NamKha hc: Ton 10Thy Lu Huy Thng

Tng i t vn: 1900 58-58-12 - Trang | 1 -

4 l do nn hc trc tuyn ti Hocmai.vn

Chng trnh hc c xy dng bi cc chuyn gia gio dc uy tn nht. i ng gio vin hng u Vit Nam. Thnh tch n tng nht: c hn 300 th khoa, khoa v hn 10.000 tn sinh vin.

Cam kt t vn hc tp trong sut qu trnh hc.

5 li ch ca hc trc tuyn

Ngi hc ti nh vi gio vin ni ting.

Chng la chn chng trnh hc ph hp vi mc tiu v nng lc.

Hc mi lc, mi ni.

Tit kim thi gian i li.

Chi ph chbng 20% so vi hc trc tip ti cc trung tm.

Tham kho cc chng trnh hc c thhu ch cho Bn

L cc kho hc trang bton bkin thc c bn theo chng trnh sch gio khoa lp 10, 11,12 tp trung vo mt skin thc trng tm ca k thi THPT quc gia.

Bn c ththam kho cc kha hc c bn lp 10, 11, 12 vi y cc mn TonVt l

Ho hcSinh hcNgvn Ting Anh tiHocmai.vn

TON VT L HO HC

SINH HC NGVN TING ANH10 11 12

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