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 33 Simplest or nicest proof that $1+x \le e^x$ 19 How can I evaluate $\sum_{n=0}^\infty (n+1)x^n$ 10 Proving $\left(\sum_{n=-\infty}^\infty q^{n^2} \right)^2 = \sum_{n=-\infty}^\infty \frac{1}{\cos(n \pi \tau)}$ 7 Showing $\frac{\sin x}{x}$ is NOT Lebesgue Integrable on $\mathbb{R}_{\ge 0}$ 7 Can someone explain Gödel's incompleteness theorems in layman terms?

### Reputation (5,101)

 +40 Expressing ${}_2F_1(a, b; c; z)^2$ as a single series +10 Confidence Level +10 Proving $\left(\sum_{n=-\infty}^\infty q^{n^2} \right)^2 = \sum_{n=-\infty}^\infty \frac{1}{\cos(n \pi \tau)}$ +5 How to show how primorials grow asymptotically?

### Questions (71)

 15 Two paradoxes: $\pi = 2$ and $\sqrt 2 = 2$ [duplicate] 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 8 GRE Math Subject Test

### Tags (145)

 62 sequences-and-series × 42 33 inequality × 3 60 calculus × 53 26 convergence × 5 42 integration × 29 22 limits × 17 39 exponential-function × 7 20 differential-equations × 16 35 complex-analysis × 20 19 power-series × 5

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 Mathematics 5,101 rep 21234 Physics 216 rep 1210 Philosophy 195 rep 14 Academia 148 rep 6 Science Fiction & Fantasy 119 rep 5