Σ_(k=0) ^∞ (k/(k^4 + 4)) = ?


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Question Number 144825 by mathdanisur last updated on 29/Jun/21

$\underset{k = 0}{\sum^{\infty}} \frac{k}{k^{4} + 4} = ?$
	Answered by Dwaipayan Shikari last updated on 29/Jun/21

	$\underset{k = 1}{\sum^{\infty}} \frac{k}{k^{4} + 4} = \frac{1}{4} \underset{k = 1}{\sum^{\infty}} \frac{1}{(k^{2} - 2 k + 2)} - \frac{1}{(k^{2} + 2 k + 2)}$ $= \frac{1}{4} (1 - \frac{1}{5} + \frac{1}{5} - . . .) = \frac{1}{4}$
	Commented by mathdanisur last updated on 29/Jun/21

	$t h a n k y o u S i r, b u t \underset{k = 0}{\sum^{\infty}}$
	Commented by Dwaipayan Shikari last updated on 29/Jun/21

	$F o r k = 0 i t i s \frac{0}{0^{4} + 4} = 0 s o i e x c l u d e d t h a t$
	Commented by mathdanisur last updated on 29/Jun/21

	$T h a n k y o u S i r$
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