Determine Whether the Series Is Convergent or Divergent by Expressing $S _ { n }$

question 109

Short Answer

Determine whether the series is convergent or divergent by expressing $S _ { n }$ as a telescoping sum. If it is convergent, find its sum.
$$\sum _ { n = 2 } ^ { \infty } \frac { 5 } { n \left( n ^ { 2 } - 1 \right) }$$