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math110

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

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93 Prove $\left(\frac{2}{5}\right)^{\frac{2}{5}}<\ln{2}$ May 3 '13
90 How prove this nice limit $\lim\limits_{n\to\infty}\frac{a_{n}}{n}=\frac{12}{\log{432}}$ Sep 9 '13
55 How to evaluate $I=\int_0^{\pi/2}x^2\ln(\sin x)\ln(\cos x)\ \mathrm dx$ Mar 14 '13
50 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
44 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
36 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
35 Surprising identities / equations Sep 26 '13
33 How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$. Jan 26 '14
33 How find this sum $\sum\limits_{n=0}^{\infty}\frac{1}{(3n+1)(3n+2)(3n+3)}$ Nov 19 '13
31 How to prove this inequality? $\frac{x^2}{y}+\frac{y^2}{z}+\frac{z^2}{x}\ge 4+(x-y)^2$ Apr 12 '14
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