Prove that: `sum_(m=1)^ntan^(-1)((2m)/(m^4+m^2+2))=tan^(-1)((n^2+n)/(n^2+n+2))`

Explanation

`∑_(m=1)^n tan^(-1) (2m) / (m^4 + m^2 + 2) `

`=(m^4 + m^2 + 2)`


`= (m^4 + 2m^2 + 1) + (- m^2 ) + 1`


`= (m^2 + 1)^2 – m^2 + 1`


`= (1 + m^2 – m) (1 + m^2 + m) + 1`
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