Mathematics
math110
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Like to share interesting and hard question and like solve math problem

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97
How prove this nice limit $\lim\limits_{n\to\infty}\frac{a_{n}}{n}=\frac{12}{\log{432}}$
Sep 9 '13
95
Prove $\left(\frac{2}{5}\right)^{\frac{2}{5}}<\ln{2}$
May 3 '13
60
How to evaluate $I=\int_0^{\pi/2}x^2\ln(\sin x)\ln(\cos x)\ \mathrm dx$
Mar 14 '13
52
Prove $\int\limits_{0}^{\pi/2}\frac{dx}{1+\sin^2{(\tan{x})}}=\frac{\pi}{2\sqrt{2}}\bigl(\frac{e^2+3-2\sqrt{2}}{e^2-3+2\sqrt{2}}\bigr)$
Mar 29 '14
47
For $a$, $b$, $c$, $d$ the sides of a quadrilateral, show $ab^2(b-c)+bc^2(c-d)+cd^2(d-a)+da^2(a-b)\ge 0$. (A generalization of IMO 1983 problem 6)
Aug 13 '13
39
Surprising identities / equations
Sep 26 '13
38
How prove this geometry inequality $R_1^4+R_2^4+R_3^4+R_4^4+R_5^4\geq {4\over 5\sin^2 108^\circ}S^2$
Apr 14 '15
34
How find this sum $\sum\limits_{n=0}^{\infty}\frac{1}{(3n+1)(3n+2)(3n+3)}$
Nov 19 '13
34
How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.
Jan 26 '14
34
Let $a, b, c$ be positive real numbers such that $abc = 1$. Prove that $a^2 + b^2 + c^2 \ge a + b + c$.
Nov 26 '13
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24
This inequality why can't solve it by now (Only four variables inequality)?
14
Find all solution $a,b,c$ with $(1-a^2)(1-b^2)(1-c^2)=8abc$
14
A variant of Cauchy-type functional equation conjecture
12
How do we show this matrix has full rank?
8
How prove this polynomial inequality from a book

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