show $(1+\frac{x}{n})^n \leq e^x$
64708
Proof that exponential function's limit definition increases monotonically?
3110
Prove $\frac{1}{\sqrt{x}}\geq \frac{\ln x}{x-1}$
87567
How to prove $1+x \leq e^x~\forall x \in \mathbb{R}?$
94119
Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$
105047
Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$
118559
Prove the inequality $\sum_{1\le i<j\le n}\sqrt{a_ia_j}<\frac{n-1}2\sum_{i=1}^n a_i$
40700
Proving inequality $(a+\frac{1}{a})^2 + (b+\frac{1}{b})^2 \geq \frac{25}{2}$ for $a+b=1$
10902
Showing that $ \prod\limits_{i=0}^{n} {n \choose i}\leq(\frac{2^n-2}{n-1})^{n-1} $
124654
Prove this inequality: $\frac n2 \le \frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac1{2^n - 1} \le n$
145274
Prove by induction $\sum \frac {1}{2^n} < 1$
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
26962
Proving an inequality involving the logarithm function: $\frac{1}{n+1} \leq \ln \left(1+\frac 1n\right) \leq \frac 1n$
36837
Prove $\frac{1+a^{2}}{1+b+c^{2}} +\frac{1+b^{2}}{1+c+a^{2}} +\frac{1+c^{2}}{1+a+b^{2}} \geq 2$
121548
proof of an inequality $ \left( 1+ \frac{x}{p} \right) ^{p}$
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
66387
Prove $(x_1+.....+x_n)^2 \leq n(x_1^2 + .....+x_n^2)$
30386
Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$