${1\over 2}\cdot{3\over 4}\dotsm{2n-1\over 2n}<{1\over \sqrt{3n+1}}$
7404
Induction and convergence of an inequality: $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}\leq \frac{1}{\sqrt{2n+1}}$
1837
Showing that $1^k+2^k + \dots + n^k$ is divisible by $n(n+1)\over 2$
142360
How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$
140983
$ \tan 1^\circ \cdot \tan 2^\circ \cdot \tan 3^\circ \cdots \tan 89^\circ$
95061
Proving that $2^{2\cdot 3^{n-1}}\equiv 1+3^n\pmod{3^{n+1}}$ for every natural $n$
12020
Prove $\sqrt{n+1}-\sqrt{n}\lt \frac{1}{2\sqrt{n}}$
131754
Prove $ \forall c \in \mathbb{R^{+}}, \forall B \in \mathbb{N}, \exists n \in \mathbb{N}, (n \geq B) \wedge (\sqrt{2n} > c \ln(n+2)) $?
110153
How to prove this inequality?$\frac{1}{n+1} + \frac{1}{n+2} + \cdots+\frac{1}{n+n} + \frac{1}{4n} > \ln 2$
62342
$x_1 \cdot \dots \cdot x_n=1 \implies x_1 + \dots + x_n \ge n$
19100
Find $\lim \limits_{n \to \infty}{1*4*7*\dots(3n+1) \over 2*5*8* \dots (3n+2)}$
19285
simplifying $ (h^2_2-h^2_3)\over ({1\over h_3})-({1\over h_2})$
120010
Show that $\aleph_{\alpha}^{\aleph_{1}} = \aleph_{\alpha}^{\aleph_{0}}\cdot 2^{\aleph_1}$
39943
Proving $\mathrm e <3$
13617
Evaluating the nested radical $ \sqrt{1 + 2 \sqrt{1 + 3 \sqrt{1 + \cdots}}} $.
33903
Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
117320
Why is this true: $\|x\|_1 \le \sqrt n \cdot \|x\|_2$?
1712
$ d_1,d_2\mid n\iff {\rm lcm}(d_1,d_2)\mid n\ $ [LCM Universal Property]