Find the sum of the series _ m=1 ^ ^ -1 ( 2m m^4+m^2+2 ).

MATHEMATICS · Subjective · AoPS · Mathematics · Sequences & Series · Sequences & Series

Problem

Find the sum of the series ∑m=1∞tan⁡−1(2mm4+m2+2).\sum_{m=1}^{\infty}\tan^{-1}\left(\frac{2m}{m^4+m^2+2}\right).

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