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Mathematics
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Tianlalu
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37
Prove $\sum_{n=1}^\infty\frac{\cot(\pi n\sqrt{61})}{n^3}=-\frac{16793\pi^3}{45660\sqrt{61}}$
Nov 30, 2018
31
Prove a strong inequality $\sum_{k=1}^n\frac{k}{a_1+a_2+\cdots+a_k}\le\left(2-\frac{7\ln 2}{8\ln n}\right)\sum_{k=1}^n\frac 1{a_k}$
Oct 12, 2018
29
On the integral $\int_0^\pi\sin(x+\sin(x+\sin(x+\cdots)))\,dx$
Oct 6, 2018
21
An interesting definite integral $\int_0^1(1+x+x^2+x^3+\cdot\cdot\cdot+x^{n-1})^2 (1+4x+7x^2+\cdot\cdot\cdot+(3n-2)x^{n-1})~dx=n^3$
Dec 4, 2016
21
On the integral $\int_{-\pi/2}^{\pi/2}\sin(x/\sin(x/\sin(x/\sin\cdots)))\,dx$
Oct 7, 2018
19
Integral $\int_0^\infty \frac{x \ln(1+x)}{(1+x)(2x^2+2x+1)} dx$
Aug 20, 2017
16
Does there exist polynomials $P$ s.t. $P(k)\mid k!$ holds for only finitely many $k\in\Bbb N$?
May 10, 2019
14
Fastest way showing the limit exists without finding the limit?
Aug 31, 2017
12
$f\left(\frac{2z}{1+z^2}\right)=\left(1+z^2\right)f(z)$, solve $f$.
Aug 18, 2017
10
Roots of $(x+a)^n+x^n+(x-a)^n=0$ are either real or purely imaginary?
Oct 10, 2018