Aryabhata

 226 Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$? 161 Comparing $\pi^e$ and $e^\pi$ without calculating them 103 Reverse Triangle Inequality Proof 82 Which one result in mathematics has surprised you the most? 78 Taking Seats on a Plane

### Reputation (70,914)

 +10 Evaluating the nested radical $\sqrt{1 + 2 \sqrt{1 + 3 \sqrt{1 + \cdots}}}$. +10 Reverse Triangle Inequality Proof +10 Is there an elementary proof that $\sum \limits_{k=1}^n \frac1k$ is never an integer? +50 For $0\lt\theta\lt1$, $\frac 1\theta\notin\mathbb Z$, there exists $f\in C[0, 1]$ such that $f(0)=f(1)$ and $f(x+\theta)-f(x)\ne0$

### Questions (12)

 66 Convergence of $\sqrt{n}x_{n}$ where $x_{n+1} = \sin(x_{n})$ 60 $5^n+n$ is never prime? 53 Evaluating $\int P(\sin x, \cos x) \text{d}x$ 52 A zero sum subset of a sum-full set 34 History of “Show that $44\dots 88 \dots 9$ is a perfect square”

### Tags (216)

 1k calculus × 152 593 integration × 45 1k real-analysis × 99 568 number-theory × 67 887 sequences-and-series × 128 488 inequality × 44 750 combinatorics × 129 484 trigonometry × 67 594 analysis × 52 450 limits × 54