$S\_1=\sum\_{n=1}^\infty \dfrac {2n+1}{n^2(n+1)^2} = ?$ 

**Attempt:** $S\_1=\sum\_{n=1}^\infty \dfrac {2n+1}{n^2(n+1)^2} = \dfrac {2n+2-1}{n^2(n+1)^2}$

$S\_1=2 \sum\_{n=1}^\infty [\dfrac {n+1}{n^2(n+1)^2} ] - \sum\_{n=1}^\infty \dfrac {1}{n^2(n+1)^2}$

$=2 \sum\_{n=1}^\infty [\dfrac {1}{n^2(n+1) } ] - \sum\_{n=1}^\infty \dfrac {1}{n^2(n+1)^2}$

I am stuck on how to move ahead. Please guide me.

Thank you for your help.