Directions: In this problem we are going to determine whether the series is convergent or divergent by expressing $s_n$ as a telescoping sum.

${\displaystyle \underset{n=2}{\overset{}{}}}\frac{2}{n^2-1}$

Calculate the partial fraction decomposition of $a_n$ :

$\frac{2}{n^2-1}=\frac{A}{n-1}+\frac{B}{n+1}$

where $A=$ and $B=$

$2.$ Calculate the partial sum:

$a_2+a_3+a_4=$

$$

$3.$ Calculate the partial sum:

$a_2+a_3+a_4+a_5=$

$$

$4.$ Determine whether the series is convergent or divergent.

If it converges, enter the sum as your answer.

If it diverges, enter divergent as your answer.

Answer $=$