$I[X,Y] :=- \sum_{x,y} p(x,y)\ln{p(x,y)}$, Show that $I[X, Y] \le I[X]+I[Y]$
31987
Conditional Entropy is less than entropy
132541
Showing ${1\over n}\sum|S_i|=O(\sqrt n)$ for $S_i\subset [n]$, $|S_i\cap S_i|\le 1$ for $i\ne j$
15943
show $\sum_{cyc}(1-x)^2\ge \sum_{cyc}\frac{z^2(1-x^2)(1-y^2)}{(xy+z)^2}.$
82621
Show $P\{\xi_1+\dots+\xi_n=1\}=(\sum_{i=1}^n \lambda_i)\Delta + O(\Delta^2)$ (Shiryaev's Probability page 44)
101499
Prove $e^{x+y}=e^{x}e^{y}$ by using Exponential Series
11289
Why $d(x) + d(y) \le n$ when proving Mantel's theorem
49408
Proof of the derivative of ln(x)
122149
How to prove that $\sum_{i<j}(X_i-X_j)^2=n\sum_{i=1}^{n}(X_i-\bar{X})^2$
138931
Show that $||x+y||\cdot||x-y||\le||x||^2+||y||^2$
5650
Show $\ln2 = \sum_\limits{n=1}^\infty\frac1{n2^n}$
84213
How to show $n\sum_{i=1}^n {x_i^2} \ge (\sum_{i=1}^n{x_i})^2$
139537
Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
53244
Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
3820
Prove that $||x|-|y||\le |x-y|$
14197
show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$
157898
Showing that $\sum_{i=1}^n \frac{1}{i} \geq \log{n}$