Determine Whether the Series $\sum _ { n = 1 } ^ { \infty } \frac { n ^ { 2 } } { 3 ( n + 1 ) ( n + 2 ) }$

Short Answer

Determine whether the series $\sum _ { n = 1 } ^ { \infty } \frac { n ^ { 2 } } { 3 ( n + 1 ) ( n + 2 ) }$ is convergent or divergent. If it is convergent, find its sum.