Proof of inequality $n!\leq(\frac{n+1}{2})^n$
72600
Proof that $n!\leq {(\frac{n+1}{2})}^{n}$
104807
Prove the inequality $\left|\frac{m}{n}-\frac{1+\sqrt{5}}{2}\right|<\frac{1}{mn}$
51730
How to prove this inequality $3^{n}\geq n^{2}$ for $n\geq 1$ with mathematical induction?
16392
Prove the Inequality on sequence
30783
Prove inequality $n<3^n$ using mathematical induction
131565
Proof by induction of summation inequality: $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\dots+\frac1{2^n}\ge 1+\frac{n}2$
26876
How to prove the inequality $2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$?
46661
A binomial inequality with factorial fractions: $\left(1+\frac{1}{n}\right)^n<\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+...+\frac{1}{n!}$
31535
Solving an inequality : $n \geq 3$ , $n^{n} \lt (n!)^{2}$.
145519
Prove that for any natural number $n>1$, we have $(2n)!<(n(n+1))^n$
20691
prove that $\frac{(2n)!}{(n!)^2}$ is even if $n$ is a positive integer
90343
Proving the inequality $|e^z-1|\leq e^{|z|}-1$
26606
Prove the inequality $\,\frac{1}{\sqrt{1}+ \sqrt{3}} +\frac{1}{\sqrt{5}+ \sqrt{7} }+\ldots+\frac{1}{\sqrt{9997}+\sqrt{9999}}\gt 24$
121544
Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
7404
Induction and convergence of an inequality: $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}\leq \frac{1}{\sqrt{2n+1}}$
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
53584
Inequality. $(n+1)\left(a^{n+1}+b^{n+1}\right) \geq (a+b)\left(a^n+a^{n-1}b+\ldots+b^{n}\right). $