J.G.

 89 What's so special about standard deviation? 63 How many “super imaginary” numbers are there? 47 An integral for the New Year 2016 45 How to attack “if true, prove it; if not true, give a counterexample” question? 44 Calculating the square root of 2

### Reputation (105,483)

 +15 I tried to prove $\sum_{n=0}^∞ \frac{n^2}{2^n} = 6$ but I feel that my proof is long. Can anyone provide an alternate proof? +10 So how exactly is the Einstein lower and upper index convention? +10 Is $\infty^\infty$ indeterminate? +10 Integral of a radial symmetric function.

### Questions (13)

 9 Do the octonions contain infinitely many copies of the quaternions? 4 Calculation in Routh's theorem 4 What's the name for this numerical integration algorithm? 3 Morrie's law with sines 3 When can limits be moved to coefficients in power series?

### Tags (656)

 1k calculus × 813 497 sequences-and-series × 265 1k integration × 652 462 trigonometry × 284 765 real-analysis × 387 405 probability × 337 511 definite-integrals × 211 397 linear-algebra × 262 498 limits × 270 339 algebra-precalculus × 193

### Bookmarks (5)

 11 prove $\int_0^\infty \frac{\log^2(x)}{x^2+1}\mathrm dx=\frac{\pi^3}{8}$ with real methods 3 Following Fibonacci 1 Studying quantized algebras, why introduce $q^{1/2}$ instead of just $q$? 1 Generative Adversarial Networks - discriminator function “running away” 0 Evaluate $\lim_{n \rightarrow \infty } \int_0^{\pi/2} \sqrt{n \sin{\frac{x}{n}} }dx$