Proving $n! < n^n$ by induction for all $n\geq 2$.
13330
Inductive Proof that $k!<k^k$, for $k\geq 2$.
15838
Induction Proof that $x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1})$
67527
Proof by Induction that $3^n ≥ 1+2^n$
71650
Proving by strong induction for a sequence of integers, $2^n$ divides term $n$
65391
Prove by induction. $n \in \mathbb N$.
85731
Prove by induction that $n! > n^2$
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
136737
Proof by Induction for inequality, $\sum_{k=1}^nk^{-2}\lt2-(1/n)$
71451
A proof by strong induction that $a_n\le3^n$ where $a_n=a_{n-1}+a_{n-2}+a_{n-3}$
102738
Show that $e^n>\frac{(n+1)^n}{n!}$ without using induction.
75329
Use induction to prove that $F_n \ge \sqrt 2 ^n$ for $n \ge 6$
101899
Proof By Induction of a Sum
49299
Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
141088
Proof : $2^{n-1}\mid n!$ if and only if $n$ is a power of $2$.
55266
Prove that $(n+1)^{n-1}<n^n$
6165
Proof by Induction $n^2+n$ is even
27580
Use mathematical induction to prove $ (2n)!\geq 2^n(n!)^2$ for $n \in \mathbb{N}$