Determine Whether the Series $\sum _ { n = 1 } ^ { \infty } \cos \left( \frac { \pi } { 2 n ^ { 2 } - 1 } \right)$

Short Answer

Determine whether the series $\sum _ { n = 1 } ^ { \infty } \cos \left( \frac { \pi } { 2 n ^ { 2 } - 1 } \right)$ is convergent or divergent. If it is convergent, find the sum.