9 A sum of Fibonacci numbers 6 The upper bound of $\lim \limits_{n\to\infty} \sum \limits_{i=1}^n e^{-i}\sqrt{i}$? 5 Dice: Rolling at least N successes where number of succeses vary by dice value 5 Functional equation $(n+1) f(n+1)= (a n+b) f(n)$ for $n=0,1,…$ 4 No non-negative continuous function on $[a,b]$ such that $\int_a^b f(t)dt=1, \int_a^b tf(t)dt=c, \int_a^b t^2f(t)dt=c^2$ for $c\in\mathbb{R}$.

### Reputation (2,932)

 +10 A “round table” dependency +50 Dice: Rolling at least N successes where number of succeses vary by dice value +30 Rate of convegence of $\frac{E^2[X^n]}{ E[X^{n-1}] E[X^{n+1}]}$ as $n \to \infty$ +10 Expectation of $\min(X,Y)$ conditional on $\max(X,Y)$

### Questions (28)

 5 A ridiculously fast way to find fixed points of the logistic function? 3 Redux: An interesting four sum inequality (feat. probability) 3 Vandermonde-type convolution with geometric term 2 Maximizing a permutation of a quadratic form 2 A “divide-and-conquer” iterative procedure for minimizing a sum of convex functions

### Tags (126)

 29 probability × 32 11 limits × 4 20 real-analysis × 11 10 summation × 4 18 inequality × 18 9 fibonacci-numbers 17 sequences-and-series × 9 8 calculus × 4 13 probability-theory × 12 8 upper-lower-bounds × 4

### Bookmarks (85)

 222 “Integral Milking” 88 Contest problem: Show $\sum_{n = 1}^\infty \frac{n^2a_n}{(a_1+\cdots+a_n)^2}<\infty$ s.t., $a_i>0$, $\sum_{n = 1}^\infty \frac{1}{a_n}<\infty$ [closed] 84 If $S$ is an infinite $\sigma$ algebra on $X$ then $S$ is not countable 82 Polynomials such that roots=coefficients 66 Stirling's formula: proof?