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AP® Calculus AB-BC

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Series: Which Diverges?

APCALC-AEX09X

Which of the following series diverges?

A

$\sum _{ n=1 }^{ \infty }{ \cfrac { { \left( -1 \right) }^{ n } }{ { 4 }^{ n } } } $

B

$\sum _{ n=1 }^{ \infty }{ \cfrac { { \left( -1 \right) }^{ n } }{ { 4n+1 } } } $

C

$\sum _{ n=1 }^{ \infty }{ \cfrac { { \left( -1 \right) }^{ n }\cdot n }{ { 4n+1 } } } $

D

$\sum _{ n=1 }^{ \infty }{ \cfrac { { \left( -1 \right) }^{ n } }{ { \sqrt [ 4 ]{ n } } } } $