proving a relation with induction , simpifying $(\sqrt x+\sqrt {x+1})^n$= $\sqrt y + \sqrt{y+1}$
50927
If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$
17491
Proof by Induction: Solving $1+3+5+\cdots+(2n-1)$
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
106993
Use Complete Induction of set theory to prove $\frac{1}{\sqrt{1}} + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + ... + \frac{1}{\sqrt{n}} > \sqrt{n}$.
115459
Proving this $F_{n+1} \cdot F_{n-1} - F^2_n = (-1)^n$ by induction
59475
Show that $\sqrt{n+1}-\sqrt{n}\to0$
57491
Double induction example: $ 1 + q + q^2 + q^3 + \cdots + q^{n-1} + q^n = \frac {q^{n+1}-1}{q-1} $
55428
Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$
122019
Prove by mathematical induction that $2^{3^n}+1$ is divisible by $3^{n+1}$
21457
Prove $\sqrt{2\sqrt{3\sqrt{\cdots\sqrt{n}}}}<3$ by induction.
81136
Prove by induction that... $1+3+5+7+...+(2n+1)=(n+1)^2$ for every $n \in \mathbb N$
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
125028
Prove the following equality using mathematical induction:
62747
Use induction to prove a product of sums of squares is a sum of squares
120093
Proof of inequality $2(\sqrt{n+1}-\sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n} - \sqrt{n-1})$ using induction
125618
Prove $2^{3^n}+1 $ is a multiple of $3^{n+1}$ by induction