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Find the sum to n terms of the series: ...

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)+`

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`T_(r)=r/(1+r^(2)+r^(4))`
`=1/2xx((r^(2)+r+1)-(r^(2)-r+1))/((r^(2)+r+1)(r^(2)-r+1))`
`=1/2[1/(r^(2)-r+1)-1/(r^(2)+r+1)]`
`=1/2[V(r-1)-V(r )]`
`thereforesum_(r=1)^(n)T_(r)=1/2(V(0)-V(n))`
`=1/2[1-1/(n^(2)+n+1)]`
`=(n^(2)+n)/(2(n^(2)+n+1))`
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