Prove $\sum\limits_{r=1}^\infty \frac{(-1)^{r+1}}{(2r-1)^3}=\frac{\pi^3}{32}$
22524
Proving that $\frac{\pi^{3}}{32}=1-\sum_{k=1}^{\infty}\frac{2k(2k+1)\zeta(2k+2)}{4^{2k+2}}$
24108
Proof of the equality $\sum\limits_{k=1}^{\infty} \frac{k^2}{2^k} = 6$
135032
Nature of the series $\sum\limits_{n=3}^{\infty} \frac{1}{(\log\log n)^{\log n}}$
17686
Evaluate the infinite series $\sum_{r=1}^{\infty} \frac{2^{-r}}{r^{2}}$
24407
How to prove the Fibonacci sum $\sum \limits_{n=0}^{\infty}\frac{F_n}{p^n} = \frac{p}{p^2-p-1}$
69084
What is the closed form for $\sum_{n=1}^\infty \frac1n - \frac1{n+1/p}$?
60197
Infinite Series $\sum\limits_{n=1}^\infty\frac{x^{3n}}{(3n-1)!}$
136444
Evaluating $\sum_{n=0}^\infty\frac{(-1)^n}{3n+1}$
72748
Proof that $\sum\limits^{\infty}_{i=0}{iP(X > i)} = \frac12(E(X²)-E(X))$ for $X$ nonnegative and integer valued
153231
Why does $\sum_1^\infty \frac1{n^3}=\frac52\sum_1^\infty\frac{(-1)^{n-1}}{n^3\binom{2n}{n}}$?
45892
arccot limit: $\sum_{r=1}^{\infty}\cot ^{-1}(r^2+\frac{3}{4})$
57372
Series convergence of $\sum_{n=1}^{\infty}\frac{1}{n^3}$
43368
How to prove $\sum\limits_{n=1}^\infty\frac{\sin(n)}n=\frac{\pi-1}2$ using only real numbers.
699
What is the value of $\sum\limits_{i=1}^\infty\frac{1}{p_{p_i}}$ where $p_{i}$ is the $i$th prime?
139430
How to prove that $\sum_{n=1}^{+\infty}\frac{1}{n^2+1}=\frac{-1+\pi \coth (\pi)}{2}$?
50812
Partial sum of the series $\sum\limits_{r=1}^{\infty} \frac{1}{r(r+1)}$
158737
What is the value of the series $\sum\limits_{n=1}^\infty \frac{(-1)^n}{n^2}$?