Show that $E(X_n)=\sum_{k=1}^{n}p^{-k}$
34046
Expected Number of Coin Tosses to Get Five Consecutive Heads
81077
Prove that $E(X^n)^{1/n}$ is non-decreasing for non-negative random variables
114031
Show that $\sum_{n=0}^\infty r^n e^{i n \theta} = \frac{1- r\cos(\theta)+i r \sin(\theta)}{1+r^2-2r\cos(\theta)}$
44328
Prove that $\sum_{k=1} ^ n k^{-1} = \ln(n) + O(1)$
13291
Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction
25654
E[X| X>Y] for independent X, Y ~ N(0,1)
101499
Prove $e^{x+y}=e^{x}e^{y}$ by using Exponential Series
36417
Why does $\mathbb{E}(\frac{X_1+...+X_n}{n})=\mathbb{E}(X)$?
61659
How to show that $ \sum_{n = 0}^{\infty} \frac {1}{n!} = e$?
105145
Show that $\mathbb{E}\left(\bar{X}_{n}\mid X_{(1)},X_{(n)}\right) = \frac{X_{(1)}+X_{(n)}}{2}$
20317
Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$
73375
Show that $\prod (1- P(A_n))=0$ iff $\sum P(A_n) = \infty$
157898
Showing that $\sum_{i=1}^n \frac{1}{i} \geq \log{n}$
84213
How to show $n\sum_{i=1}^n {x_i^2} \ge (\sum_{i=1}^n{x_i})^2$
4991
Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$
112005
Showing that if $p_1 + \cdots p_n = 1$ then $\displaystyle \sum_{k=1}^n \left(p_k + \dfrac {1}{p_k} \right)^2 \ge n^3+2n+\dfrac 1n$?
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$