Proof that $P(X\geq 2^{-n})\leq 2^nE X$
50830
Case of equality in Markov's inequality
7448
Prove $S \doteq \sum_{n=1}^{\infty} p_n  0$ assuming $0 \leq p_n < 1$.
4776
Prove that the power set of an $n$-element set contains $2^n$ elements
91740
Hadamard's inequality proof
142785
How can I prove Holder inequality for $0<p<1$?
119436
Proving $2^n\leq 2^{n+1}-2^{n-1}-1$ for all $n\geq 1$ by induction
25419
If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$
128558
Inequality between $\ell^p$-norms
51730
How to prove this inequality $3^{n}\geq n^{2}$ for $n\geq 1$ with mathematical induction?
27570
Prove $(1-x)\ln(1-x)+(1+x)\ln(1+x)\leq 2x^2$ for $0<x<1$
47895
Prove $\lim\limits_{n\to\infty}n^{-1/(p+1)}(1^{1^p}\cdot 2^{2^p}\cdots n^{n^p})^{n^{-p-1}}=e^{-1/(p+1)^2}$
148458
$x^p-x \equiv x(x-1)(x-2)\cdots (x-(p-1))\,\pmod{\!p}$
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
119118
Prove $n\mid \phi(2^n-1)$
8609
Prove by induction that $n!>2^n$
10902
Showing that $ \prod\limits_{i=0}^{n} {n \choose i}\leq(\frac{2^n-2}{n-1})^{n-1} $