Gautam Shenoy
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 28 Why is $i^3$ (the complex number “$i$”) equal to $-i$ instead of $i$? 16 Proving there are no integers $a, b, c$ satisfying $12a + 18b + 27c = 227$ 13 Prove that $\frac{mn}{1+m+n}\ge\frac{1}{3}$ for $m,n\in\mathbb{N}$ 10 Is linear function convex or concave? 10 $\lim_{R\rightarrow\infty} \int_0^R e^{x^2 - R^2}dx$

### Reputation (5,368)

 +8 Finding the finite product $\prod_{k=2}^{\infty}\frac{k^2}{k^2-1}$. +10 Function of Determinant convexity via information theoretic methods +10 An elementary proof for a bound on $x \log x$ +10 Does $\sum \frac{(n+4^n)}{n+6^n}$ converge or diverge?

### Questions (44)

 12 cosh x inequality 8 To show that $P(|X-Y| \leq 2) \leq 3P(|X-Y| \leq 1)$ 6 Limit of a sequence involving root of a factorial: $\lim_{n \to \infty} \frac{n}{ \sqrt [n]{n!}}$ [duplicate] 6 Showing $2^{n_2} + 3^{n_3}+\cdots+9^{n_9}$ is dense in $\mathbb{R}^+$ 6 Application of Central Limit Theorem

### Tags (115)

 82 real-analysis × 39 30 complex-numbers × 5 53 calculus × 22 28 fake-proofs × 2 51 probability × 34 27 sequences-and-series × 18 36 probability-theory × 32 24 algebra-precalculus × 9 35 elementary-number-theory × 10 23 inequality × 13

### Accounts (4)

 Mathematics 5,368 rep 1032 Arqade 101 rep 3 Role-playing Games 101 rep 1 MathOverflow 101 rep 1