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visits member for 2 years, 7 months
seen Apr 3 at 12:24

I have given up mathematics after highschool but still it is a great hobby. I am mainly interested in inequalities, euclidean geometry and combinatorics.


Jan
28
answered Prove $\left(\sum_{1 \le i <j \le n} |x_i-x_j|\right)^2 \ge (n-1)\sum_{1\le i<j \le n} (x_i-x_j)^2.$
Jan
28
revised Prove that $\,\,\displaystyle\inf_{n\in\mathbb N}\sum_{k=0}^{p}\lvert\sin{(n+k)^p}\rvert>0$
added tag inequality
Jan
28
suggested suggested edit on Prove that $\,\,\displaystyle\inf_{n\in\mathbb N}\sum_{k=0}^{p}\lvert\sin{(n+k)^p}\rvert>0$
Jan
23
answered Inequality $ \left|x\sin\frac{1}{x}-y\sin\frac{1}{y}\right|\leq\sqrt{2|x-y|} $
Oct
31
awarded  Revival
Sep
13
comment How to prove $\prod_{i=1}^{n}\left(\dfrac{x_{i}}{\sin{x_{i}}}\right)^{2a_{i}}+\prod_{i=1}^{n}\left(\dfrac{x_{i}}{\tan{x_{i}}}\right)^{a_{i}}>2$?
I suggest to try to prove that $(\frac{x}{sin(x)})^{2a}+(\frac{x}{tan(x)})^a$ is increasing (in $x$ and in $a$) and hence always bigger than 2.
Sep
13
comment How to prove $\prod_{i=1}^{n}\left(\dfrac{x_{i}}{\sin{x_{i}}}\right)^{2a_{i}}+\prod_{i=1}^{n}\left(\dfrac{x_{i}}{\tan{x_{i}}}\right)^{a_{i}}>2$?
Hey, this is a nice document. Is it possible to be downloaded? I can't understand because of the Chinese...
Aug
31
awarded  Yearling
Aug
16
answered Prove the Inequality: $\sum\frac{x^3}{2x^2+y^2}\ge\frac{x+y+z}{3}$
Aug
9
comment Azuma's inequality to McDiarmid's inequality?
Have you looked at the original McDiarmid paper? I have uploaded it for you here.
Aug
9
answered The definition of “number”
Aug
7
answered Proving Jensen's inequality.
May
17
awarded  Caucus
Apr
27
answered How to prove $\frac{\pi^2}{6}\le \int_0^{\infty} \sin(x^{\log x}) \ \mathrm dx $?
Apr
26
revised cauchy schwarz inequality problemes
edited tags
Apr
24
revised $a_1t^k\leq-\sqrt{1+x^2}+x\operatorname{arcsinh}{x}+1\leq a_2t^k,\ \forall\ t\in[0,\epsilon]$?
expanded answer
Apr
24
answered $a_1t^k\leq-\sqrt{1+x^2}+x\operatorname{arcsinh}{x}+1\leq a_2t^k,\ \forall\ t\in[0,\epsilon]$?
Apr
24
comment $a_1t^k\leq-\sqrt{1+x^2}+x\operatorname{arcsinh}{x}+1\leq a_2t^k,\ \forall\ t\in[0,\epsilon]$?
I gotta ask - did you try to plug in a series expansion?
Apr
24
comment $a_1t^k\leq-\sqrt{1+x^2}+x\operatorname{arcsinh}{x}+1\leq a_2t^k,\ \forall\ t\in[0,\epsilon]$?
$t$ and $x$ seem independent. I think this is a typo... can you update your question?
Feb
7
answered Prove or disprove an inequality with $0 \le a_1 \le a_2 \le \ldots \le a_n$