Calculus II Infinite Series GPC-Dunwoody LTC
Convergence Tests
n-th Term Test: DNEor 0lim if diverges n1
= nn
n aa
Integral Test: [ ) )( and ,1for decreasing positive, ,continuous
)( nfaxxf n =
(diverges) converges then ,(diverges) converges )( If 11 =
nnadxxf
Comparison Test:
diverges allfor and diverges b)2
converges allfor and converges b 1) then , allfor 0 and
n
n
nnn
nnn
nn
anba
anbanba
Limit Comparison Test:
>=>
divergeboth or convergeboth and then
finite) ( ,0lim and 0, Ifn
nn
n
nnn
ba
ccbaba
Alternating Series Test: converges )1(0lim
0
1
11
=
+
=>
nn
n
nn
nn
n
bb
bbb
Absolute Convergence Test: converges converges nn aa Ratio Test:
Root Test:
veinconclusi1diverges or 1
convergent absolutely is 1
Then . limLet 1
==>
