Upper bound of $\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{4}\right)...\left(1+\dfrac{1}{2^n}\right)$
60024
Proof that a sequence is convergent
36837
Prove $\frac{1+a^{2}}{1+b+c^{2}} +\frac{1+b^{2}}{1+c+a^{2}} +\frac{1+c^{2}}{1+a+b^{2}} \geq 2$
48503
Proving : $ \bigl(1+\frac{1}{n+1}\bigr)^{n+1} \gt (1+\frac{1}{n})^{n} $
108782
Inequality $\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1} \ge 1$
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
67650
Short and intuitive proof that $\left(\frac{n}{k}\right)^k \leq \binom{n}{k}$
2708
Inequality ${n \choose k} \leq \left(\frac{en}{ k}\right)^k$
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
2414
If $f \in \operatorname{Hol}(D)$, $f(\frac{1}{2}) + f(-\frac{1}{2}) = 0$, prove that $|f(0)| \leq \frac{1}{4}$
118674
Simple upper bound for $\binom{n}{k}$
7404
Induction and convergence of an inequality: $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}\leq \frac{1}{\sqrt{2n+1}}$
81842
How to prove by induction that $\frac{a^n+b^n}{2}\geq\left(\frac{a+b}{2}\right)^n$?
117370
$\lim_{n\to\infty} \left(1+\frac{2}{n}\right)^{n^2} e^{-2n}$
5072
To evaluate limit of sequence $\left(\left( 1 + \frac1n \right) \left( 1 + \frac2n \right)\cdots\left( 1 + \frac nn \right) \right)^{1/n}$
27347
Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.
145909
Prove that $\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+....+\frac{1}{2n}\geq \frac{2}{3}$
66247
Proving inequality $\left( \frac {x} {y}\right) ^{x}\left( \frac {1-x} {1-y}\right) ^{1-x}\geqslant 1$