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 43 Simplest or nicest proof that $1+x \le e^x$ 39 How can I evaluate $\sum_{n=0}^\infty (n+1)x^n$ 12 Proving $\left(\sum_{n=-\infty}^\infty q^{n^2} \right)^2 = \sum_{n=-\infty}^\infty \frac{1}{\cos(n \pi \tau)}$ 10 Showing $\frac{\sin x}{x}$ is NOT Lebesgue Integrable on $\mathbb{R}_{\ge 0}$ 9 Can someone explain Gödel's incompleteness theorems in layman terms?

### Reputation (6,022)

 +10 Simplest or nicest proof that $1+x \le e^x$ +10 Proving $\left(\sum_{n=-\infty}^\infty q^{n^2} \right)^2 = \sum_{n=-\infty}^\infty \frac{1}{\cos(n \pi \tau)}$ +10 How can I evaluate $\sum_{n=0}^\infty (n+1)x^n$ +10 Big-O Interpretation

### Questions (75)

 18 Two paradoxes: $\pi = 2$ and $\sqrt 2 = 2$ [duplicate] 10 GRE Math Subject Test 9 Interesting sum-integral equality 8 Expressing ${}_2F_1(a, b; c; z)^2$ as a single series 8 Concerning the classical normalized Eisenstein series

### Tags (146)

 92 sequences-and-series × 43 42 inequality × 4 62 calculus × 54 40 complex-analysis × 23 49 exponential-function × 7 39 power-series × 5 48 convergence × 6 39 faq 47 integration × 29 22 limits × 17

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 Mathematics 6,022 rep 21637 Philosophy 260 rep 115 Physics 236 rep 1210 Academia 153 rep 7 Science Fiction & Fantasy 119 rep 5