ᴊ ᴀ s ᴏ ɴ

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I'm deeply impressed by mathematics.

171 Questions

 21 Seems that I just proved $2=4$. 16 Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer. 15 Show that $\sqrt[3]{2+\frac {10} 9\sqrt 3}+\sqrt[3]{2-\frac {10} 9\sqrt 3}=2$ 15 Solve $x^x=2x$ where $x\in\mathbb C$. 14 Show that $\frac 1 {\sqrt{x+y}}+\frac 1 {\sqrt{y+z}}+\frac 1 {\sqrt{z+x}}\geq2+\frac 1 {\sqrt2}$.

4,557 Reputation

 +30 How to prove $\int^1_0\int^1_0\frac{\log(x-x^2)-\log(y-y^2)}{(x-x^2)-(y-y^2)}dxdy=7\sum_{i=1}^\infty i^{-3}$? +20 What's the number of possible structures of alkanes $C_n H_{2n+2}$? +5 How show $\mathbb N \cong \mathbb Q$ using Cantor pairing? +5 Show that $(x_n-y_n)$ converges to $x-y$.

 24 Why does $\tan^{-1}(1)+\tan^{-1}(2)+\tan^{-1}(3)=\pi$? 10 How to simplify an expression like this: $(x^2+x^{-2}-2)^{1/2}$ 8 Evaluating tetration to infinite heights (e.g., $2^{2^{2^{2^{.^{.^.}}}}}$) 7 Show that $d/dx (a^x) = a^x\ln a$. 6 How to prove two trigonometric identities

77 Tags

 33 trigonometry × 12 8 exponentiation × 2 29 algebra-precalculus × 34 8 recursion 25 calculus × 30 6 polynomials × 4 18 sequences-and-series × 19 6 roots × 3 11 homework × 16 5 integration × 11

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