Prove by induction that for $n\geq1$, $(a_1+a_2+...+a_n)/n \geq (a_1*a_2*...*a_n)^{1/n}$
61635
Proving AM-GM with induction
16798
Prove the inequality $n! \geq 2^n$ by induction
101899
Proof By Induction of a Sum
11642
Proving by induction that $2^n \le 2^{n+1}-2^{n-1} - 1$ . Does my proof make sense?
106502
Prove by induction that for the Fibonacci numbers $F(n)$ with $n \ge 6$, $F(n) \ge 2^{n/2}$
108298
Prove $\sum_{i=1}^{i=n}\frac{a_i}{S-a_i}\geqslant \frac{n}{n-1}$ and $\sum_{i=1}^{i=n}\frac{S-a_i}{a_i}\geqslant n(n-1)$.
121544
Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
33082
Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.
139269
Prove that $2n-3\leq 2^{n-2}$ , for all $n \geq 5$ by mathematical induction
18301
Proof by Induction involving Inequality and Factorials as denominators
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
81136
Prove by induction that... $1+3+5+7+...+(2n+1)=(n+1)^2$ for every $n \in \mathbb N$
13291
Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
96332
Prove by induction that $\sqrt[n+1]{n+1}<\sqrt[n]{n}$ for $n\ge 3$
51730
How to prove this inequality $3^{n}\geq n^{2}$ for $n\geq 1$ with mathematical induction?
55273
Prove by mathematical induction that: $\forall n \in \mathbb{N}: 3^{n} > n^{3}$