# ᴊ ᴀ s ᴏ ɴ

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I'm deeply impressed by mathematics.

# 187 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. 16 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 $\frac 1 {\sqrt{x+y}}+\frac 1 {\sqrt{y+z}}+\frac 1 {\sqrt{z+x}}\geq2+\frac 1 {\sqrt2}$.

# 4,842 Reputation

 -4 Prove that intersection of connected spaces is connceted. +5 Show that $Int(A)=X\setminus\overline{X\setminus A}$. +5 Show that $\sqrt[3]{2+\frac {10} 9\sqrt 3}+\sqrt[3]{2-\frac {10} 9\sqrt 3}=2$ +5 Show that $\overline{A\cap B}\subseteq\bar{A}\cap\bar{B}$

 27 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., $2^{2^{2^{2^{.^{.^.}}}}}$) 8 Show that $d/dx (a^x) = a^x\ln a$. 6 How to prove two trigonometric identities

# 82 Tags

 37 trigonometry × 12 8 exponentiation × 2 33 algebra-precalculus × 35 8 recursion 26 calculus × 30 6 integration × 11 18 sequences-and-series × 19 6 polynomials × 4 16 homework × 17 6 roots × 3

# 5 Accounts

 Mathematics 4,842 rep 2939 Chemistry 113 rep 4 Physics 107 rep 3 Mathematica 107 rep 3 TeX - LaTeX 101 rep