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Question Number 73774 by mind is power last updated on 15/Nov/19

hello, show that

\sum_{n ⩾ 1} \frac{{(- 1)}^{n} nsin (n)}{1 + n^{2}} = \frac{π e^{1} - π e^{- 1}}{- {2 e}^{π} + {2 e}^{- π}}

indication, Residus Theorem let

f (z) = \frac{zsin (z)}{(1 + z^{2}) \sin (π z)}

have a very nice day!