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**mathaddict** If $\displaystyle f(r)=\frac{1}{r^2}$ , simpify f(r)-f(r+1) . Hence , find the sum of the first n terms of the series

$\displaystyle

\frac{3}{1^2\times2^2}+\frac{5}{2^2\times3^2}+\fra c{7}{3^2\times4^2}+...

$

My working :

After simplifying , i got $\displaystyle \frac{2r+1}{r^2(r+1)^2}$ .

Afrer doing the partial fraction , i got

$\displaystyle \sum^{n}_{r=1}\frac{2r+1}{r^2(r+1)^2}=\sum^{n}_{r= 1}[\frac{1}{r^2}-\frac{1}{r+1}\frac{1}{(r+1)^2}]$

I need help on finding the sums , i am not sure how to continue from where i stopped and i am not sure how to use the method of differences here . THanks for any help