Find the sum to `n` terms of the series `3//(1^2xx2^2)+5//(2^2xx3^2)+7//(3^2xx4^2)+dot`

Explanation

`T_(r)=((2r+1))/(r^(2)(r+1)^(2))`
`=((r+1)^(2)-r^(2))/(r^(2)(r+1)^(2))`
`=1/r^(2)-1/((r+1)^(2))`
`=V(r )-V(r+1)`
`thereforesum_(r=1)^(n)T_(r)=sum_(r=1)^(n)[1/r^(2)-1/((r+1)^(2))]`
`=1-1/((n+1)^(2))`
`=(2n+n^(2))/((n+1)^(2))`
Also, `sum_(r=1)^(oo)T_(r)=lim_(ntooo)(2n+n^(2))/(n^(2)+2n+1)lim_(ntooo)(2/n+1)/(1+2/n+1/n^(2))=1`