Find the sum to n terms of the series
`1/(1+1^(2)+1^(4))+2/(1+2^(2)+2^(4))+3/(1+3^(2)+3^(4))+… .`

Explanation

The nth term of the given series is `T_(n)=(n)/(1+n^(2)+n^(4))`
`:.`Sum of n terms `S_(n)=sumT_(n)=sum(n)/(1+n^(2)+n^(4))`
`=sum(n)/((1+n+n^(2))(1-n+n^(2)))`
`=(1)/(2)sum((1)/(1+n+n^(2))-(1)/(1-n+n^(2)))`
`=(1)/(2)((1)/(1-1+1)-(1)/(1+n+n^(2))) " " [" by property"]`
`=((n+n^(2)))/(2(1+n+n^(2)))=(n(n+1))/(2(n^(2)+n+1))`.