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Find the interval of convergence for the power series $\sum _{ n=1 }^{ \infty }{ \cfrac { { \left( 3x+1 \right) }^{ n } }{ { n }^{ 2 } } } $.

$\cfrac { 2 }{ 3 } \ < \ x \ < \ 0$

$-\cfrac { 2 }{ 3 } \le \ x \ \le \ 0$

$-\infty \ < \ x \ < \ \infty $

$-1 \ < \ x \ < \ 3$