$n>2\rightarrow{2^{n}\leq(2n)^{\pi(2n)}\land n^{\pi(2n)-\pi(n)}<2^{2n}}$
34017
Show that $n^{\pi\left(2n\right)-\pi\left(n\right)}2$
1478
An inequality for powers of reals: $a^{1/n}-b^{1/n}<(a-b)^{1/n}$
33903
Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
120795
Showing that $\sin^2x\cdot\sin^22x\cdot\sin^24x\cdot\sin^28x\cdots\sin^22^nx\leq\frac{3^n}{4^n}$
77510
$\sum_{1}^{n}\left ( a_{i}b_{i} \right )\geq \prod_{1}^{n}\left ( a_{i}^{b_{i}} \right )$
127047
How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
148163
Show that if m/n is a good approximation of $\sqrt{2}$ then $(m+2n)/(m+n)$ is better
129890
Proving inequality $|\sin(n\theta) |\le n\sin\theta$
42292
Show that $a_n<\sqrt{2}$ for every $n\in\mathbb{N}$.
118244
An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
10902
Showing that $ \prod\limits_{i=0}^{n} {n \choose i}\leq(\frac{2^n-2}{n-1})^{n-1} $
120093
Proof of inequality $2(\sqrt{n+1}-\sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n} - \sqrt{n-1})$ using induction
24403
Prove that $ n < 2^{n}$ for all natural numbers $n$.
98242
Integral inequality in $\Bbb R^n$
51129
Proving $n^\epsilon > \log(n)$ for sufficiently large $n$
50781
$(n+1)$th prime $p_{n+1}$ less than or equal to $p_1p_2\dots p_n+1$
108995
Prove $|e^{i\theta} -1| \leq |\theta|$