Prove the inequality for n>2.
2554
Show that if $n>2$, then $(n!)^2>n^n$.
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
59905
Proving the inequality $\frac{n^k}{k^k}\leq\binom{n}{k}\leq\frac{n^k}{k!}$ involving binomial coefficient.
77091
Inequality $\binom{2n}{n}\leq 4^n$
149216
Give a combinatorial proof to show the following for all integers $n \geq 2$.
118559
Prove the inequality $\sum_{1\le i<j\le n}\sqrt{a_ia_j}<\frac{n-1}2\sum_{i=1}^n a_i$
136274
$n! \leq \left( \frac{n+1}{2} \right)^n$ via induction
156669
Trying to prove a simple (?) inequality
11867
Prove by induction that $n < 2^n$ for all $n \ge 1$
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
126889
Proof by induction: inequality $n! > n^3$ for $n > 5$
107335
Prove equality between binomial coefficients.
48092
Inequality involving a finite sum
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
105268
prove inequality through mean value theorem
66387
Prove $(x_1+.....+x_n)^2 \leq n(x_1^2 + .....+x_n^2)$
12781
Prove the following inequality $\sqrt[n]{x_1x_2...x_n}\ge (n-1)$