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

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

A

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

B

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

C

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

D

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

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