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AP® Calculus AB-BC

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Moderate

Converging Ratio Test

APCALC-JG02RD

Find all values of $x$ for which the following series converges.

$$\sum _{ n=1 }^{ \infty }{ \cfrac { { 3 }^{ n }{ x }^{ n } }{ n+1 } } $$

A

$ (-\cfrac{1}{3}, \cfrac{1}{3})$

B

$[-\cfrac{1}{3},\cfrac{1}{3}]$

C

$(-\cfrac{1}{3},\cfrac{1}{3}]$

D

$[-\cfrac{1}{3},\cfrac{1}{3})$