Proof: $\sqrt[n]{n} > \sqrt[n+1]{n+1}$
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
42976
How do you prove the follwing $|\sqrt[n]{x}-\sqrt[n]{y}| \le \sqrt[n]{|x-y|}$
55266
Prove that $(n+1)^{n-1}<n^n$
5728
How to prove $\lim_{n \to \infty} \sqrt{n}(\sqrt[n]{n} - 1) = 0$?
42292
Show that $a_n<\sqrt{2}$ for every $n\in\mathbb{N}$.
117640
Prove that $\lim \inf \dfrac{x_{n+1}}{x_n}\leq \lim \inf x_n^{1\over n} \leq \lim \sup x_n^{1\over n} \leq \lim \sup \dfrac{x_{n+1}}{x_n}. $
52157
Prove that $d(n)\leq 2\sqrt{n}$
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
21457
Prove $\sqrt{2\sqrt{3\sqrt{\cdots\sqrt{n}}}}<3$ by induction.
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
71639
Proof $(1+1/n)^n$ is an increasing sequence
61472
If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$
127955
Show that $\sqrt{1+n(n+1)(n+2)(n+3)}$ is a whole number for all whole numbers $n$.
121544
Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
148582
Proof: $\|X\|_2\leq \sqrt{n}\|X\|_\infty$
62556
Prove $3|n(n+1)(n+2)$ by induction
54659
How prove that $(a_{n})_{n \in \mathbb{N}}$ is convergent with $a_{0}=1$, $a_{n+1}= \sqrt{2a_{n}}$?