Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
21986
What is the minimum value of $(1 + a_1)(1 + a_2). . .(1 + a_n)$?
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
63523
$|a_{n+1}-a_n| \leq \frac{1}{2} |a_{n}-a_{n-1}|$. Prove $(a_n)$ is Cauchy
12781
Prove the following inequality $\sqrt[n]{x_1x_2...x_n}\ge (n-1)$
35564
Prove that $u\cdot v = \frac{1}{4}||u+v||^2 - \frac{1}{4}||u-v||^2 \forall u,v \in \mathbb{R^n}$
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
27922
prove that $\binom{n}{0}^2+\binom{n}{1}^2+\binom{n}{2}^2+\cdots+\binom{n}{n}^2=\binom{2n}{n}$
111515
Proving that $-a=(-1)\cdot a$
66082
Using $\sqrt{1-t}\leq 1-\frac t2$ to show that $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots2n}\geq\frac1{2\sqrt n}$
118559
Prove the inequality $\sum_{1\le i<j\le n}\sqrt{a_ia_j}<\frac{n-1}2\sum_{i=1}^n a_i$
48503
Proving : $ \bigl(1+\frac{1}{n+1}\bigr)^{n+1} \gt (1+\frac{1}{n})^{n} $
139383
Prove that $\tau(2^n-1) \geq \tau(n)$ for all positive integers $n$.
62342
$x_1 \cdot \dots \cdot x_n=1 \implies x_1 + \dots + x_n \ge n$
151520
About the parity of the product $(a_1-1)(a_2-2)\cdots(a_n-n)$
18477
$(W_1+W_2+\cdots+W_n)^a \leq W_1^a +\cdots + W_n^a$ for $n$ integer, $n\geq 2$, $W\gt 0$ and $a$ constant, real, $0\lt a\lt 1$
7404
Induction and convergence of an inequality: $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}\leq \frac{1}{\sqrt{2n+1}}$
90496
Proving $\lim \frac{x^n-a^n}{x-a}=n\cdot a^{n-1}$