Mathsource

# 28 Questions

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### How I can calculate $\sum_{n = 0}^{\infty}\frac{(-1)^n(2n + 1)}{n^2 + 1}$

Jul 24 at 19:56 Mathsource 3,395
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### Prove that $\sum_{n=1}^{\infty}(-1)^{n+1}\frac{\ln(2n+1)}{2n+1} = \frac{\pi}{4}(\gamma - \ln \pi) + \pi \ln \Gamma(\frac{3}{4})$

Jul 4 at 15:57 StubbornAtom 7,778

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### Calculate in closed form: $\int_{0}^{\pi/2}\arctan\left(\frac{1}{\sqrt{2\sin x}}\right)dx$

Mar 4 at 19:28 clathratus 6,824
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### How to show $\sum_{n=2}^{\infty}(-1)^n \frac{\log(n)}{n} = \gamma \log(2) - \frac{\log^2(2)}{2}$?

Jan 23 at 20:46 Mathsource 3,395
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