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10
Sum inequality: $\sum_{k=1}^n \frac{\sin k}{k} \le \pi-1$
6
How to prove that $\int_0^1\left(\sum_{k=n}^\infty {x^k\over k}\right)^2\,dx = \int_0^1 2x^{n-1}\log\left(1+{1\over\sqrt{x}}\right)\,dx.$
5
Prove $\sum_{i=1}^{n}\frac{x_{i}^3}{x_{i+1}^2}\geq \sum_{i=1}^{n}\frac{x_{i}^2}{x_{i+1}}$
4
Two curious “identities” on $x^x$,$e$,and $\pi$
2
An Inequality problem relating $\prod\limits^n(1+a_i^2)$ and $\sum\limits^n a_i$
2
Compute $\lim_{n\to\infty} \sum_{k=1}^{n} \left(\frac{k}{n^2}\right)^{\left(\frac{k}{n^2} + 1\right)}$
2
Why does the equation $x^2-82y^2=\pm2$ have solutions in every $\mathbb{Z}_p$ but not in $\mathbb{Z}$?
2
Computing $ \int_0^{\infty} \frac{ \sqrt [3] {x+1}-\sqrt [3] {x}}{\sqrt{x}} \mathrm dx$
2
Convex Alternatives to the Gamma Function?
2
Root of a special polynomial
1
How to prove $\frac{a}{a+bc}+\frac{b}{b+ac}+\frac{c}{c+ab}\geq \frac{3}{2}$
1
Inequality. $\frac{(b+c)^2}{a^2+bc}+\frac{(c+a)^2}{b^2+ca}+\frac{(a+b)^2}{c^2+ab} \geq 6 $
1
$G$ is a finite group. $ H,K \leq G $ and $ K \lhd G $. $G:H$ and $|K|$ are coprime. Show that $K \leq H $
0
Prove that $\frac{1}{\sin^2 z } = \sum\limits_{n= -\infty} ^ {+\infty} \frac{1}{(z-\pi n)^2} $
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