Proof $a_{n+1} \geq a_n$ with $a_n := (1+1/n)^n$ for $n \in \mathbb{N}$
25921
Show that $\left(1+\dfrac{1}{n}\right)^n$ is monotonically increasing
60036
How to prove this limit exists: $a_{n+2}=\sqrt{a_{n+1}}+\sqrt{a_{n}}$
116966
Prove $\limsup_{n \rightarrow \infty} a_n\geq1$ if $\lim_{n \rightarrow \infty} a_na_{n+1}=1$
84283
If $a\neq 1$, find $(a+1)(a^2+1)(a^4+1)\ldots(a^{2^n}+1)$.
25648
Prove $(a_1+b_1)^{1/n}\cdots(a_n+b_n)^{1/n}\ge \left(a_1\cdots a_n\right)^{1/n}+\left(b_1\cdots b_n\right)^{1/n}$
12096
If $a+1/a$ is an integer, then so is $a^t+1/a^t$ for $t\in\mathbb N$
106767
$|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
119436
Proving $2^n\leq 2^{n+1}-2^{n-1}-1$ for all $n\geq 1$ by induction
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
81842
How to prove by induction that $\frac{a^n+b^n}{2}\geq\left(\frac{a+b}{2}\right)^n$?
96332
Prove by induction that $\sqrt[n+1]{n+1}<\sqrt[n]{n}$ for $n\ge 3$
50673
Limit of ${a_n}^{1/n}$ is equal to $\lim_{n\to\infty} a_{n+1}/a_n$
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
8814
Proving that a sequence such that $|a_{n+1} - a_n| \le 2^{-n}$ is Cauchy
16798
Prove the inequality $n! \geq 2^n$ by induction
53918
whats the proof for $\lim_{x → 0} [(a_1^x + a_2^x + .....+ a_n^x)/n]^{1/x} = (a_1.a_2....a_n)^{1/n}$
78144
How to prove the inequality $a_1^{a_1}a_2^{a_2}\cdots a_n^{a_n} > \left(\frac{a_1+\dots+a_n}{n}\right)^{a_1+\dots+a_n}$?