81 Can we calculate $i\sqrt { i\sqrt { i\sqrt { \cdots } } }$? 51 Prove that every positive integer divides a number such as $70, 700, 7770, 77000$. 35 Why do these paths all have the same length? 21 If $u_1=1$ and $u_{n+1} = n+\sum_{k=1}^n u_k^2$, then $u_n$ is never a square. 17 How to find $x$ given $\log_{9}\left(\frac{1}{\sqrt3}\right) =x$ without a calculator?

### Reputation (31,446)

 +10 Does a right angle triangle ABC, right angled at A has A-symmedian? +10 What is $a_n$, if $\sum_0^\infty a_n x^n = (\sum_0^\infty x^n )(\sum_0^\infty x^{2n})$ +10 Compute $\prod_{n=2}^{\infty}\left(1-\frac{1}{n^2}\right).$ +10 Sum of integrals probably converges to $\ln(2)$ (Seemous 2018-2019)

### Questions (7)

 28 Is there a closed-form solution for $\sum_{n=1}^{\infty} \sum_{m=1}^{\infty} \frac{1}{nm(3n+m)}$? 10 A double sum or a definite integral. 6 Elliptic Integrals & Gamma Functions of Rational values. 4 A double sum for the square of the natural logarithm of $2$. 4 Show the integral identity $\int_0^1 \frac{\ln(1-x) (\ln(1+x))^2}{x} dx = -\frac{\pi^4}{240}$ [duplicate]

### Tags (365)

 377 combinatorics × 197 157 number-theory × 56 310 algebra-precalculus × 112 149 elementary-number-theory × 60 227 sequences-and-series × 114 128 inequality × 89 192 summation × 68 119 complex-numbers × 26 159 calculus × 94 117 discrete-mathematics × 73

### Bookmarks (17)

 29 What is the binomial sum $\sum_{n=1}^\infty \frac{1}{n^5\,\binom {2n}n}$ in terms of zeta functions? 18 A sequence with dominoes 17 What is $\int_0^1 \frac{\log \left(1-x^2\right) \sin ^{-1}(x)^2}{x^2} \, dx$? 14 On binomial sums $\sum_{n=1}^\infty \frac{1}{n^k\,\binom {2n}n}$ and log sine integrals 12 Conjecture about distribution of certain primes