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Question Number 129651 by mnjuly1970 last updated on 17/Jan/21

              ... nice   calculus...      evaluate ::          Σ_(n=1) ^∞  (((−1)^n )/(n^2 +1)) (((sin(n))/n))^2 =?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:{nice}\:\:\:{calculus}... \\ $$$$\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} +\mathrm{1}}\:\left(\frac{{sin}\left({n}\right)}{{n}}\right)^{\mathrm{2}} =? \\ $$$$ \\ $$

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