Proof of $n^{1/n} - 1 \le \sqrt{\frac 2n}$ by induction using binomial formula
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
121874
Use Induction to prove that for all $n \in \mathbb{N}, (x^n + \frac{1}{x^n}) \in \mathbb{Z}$ if $x+\frac{1}{x}\in\mathbb{Z}$.
128309
Use Mathematical Induction to prove that $\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} +...+\frac{1}{n(n+1)}=1-\frac{1}{n+1}$
14435
Show by induction: $(1+\frac{1}{n})^{n}<n$
63510
Prove: $\binom{n}{k}^{-1}=(n+1)\int_{0}^{1}x^{k}(1-x)^{n-k}dx$ for $0 \leq k \leq n$
145274
Prove by induction $\sum \frac {1}{2^n} < 1$
12020
Prove $\sqrt{n+1}-\sqrt{n}\lt \frac{1}{2\sqrt{n}}$
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
64437
Proof by induction (power rule of the derivative)
66019
Revisited: Binomial Theorem: An Inductive Proof
13291
Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction
27304
Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction
25054
Proving $\frac{1}{n+1} + \frac{1}{n+2}+\cdots+\frac{1}{2n} > \frac{13}{24}$ for $n>1,n\in\Bbb N$ by Induction
128913
A proof of $\sum_{i=1}^{n}(-1)^{i-1}\binom{n}{i}\frac{1}{i}=\frac{1}{1}+\frac{1}{2}+....+\frac{1}{n}$
15838
Induction Proof that $x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1})$
63652
Mathematical induction for inequalities: $\frac1{n+1} + \frac1{n+2} + \cdots +\frac1{3n+1} > 1$
91197
Proving $n! \ge 2^{n-1 }$for all $n\ge1 $by mathematical Induction