Proving $2^n<n!$ using simple induction.
8609
Prove by induction that $n!>2^n$
68480
Proof by Induction: Prove that $2^n > n^2$, for all natural numbers greater than or equal to $5$
44906
Use induction to prove that $2^n$ divides $(2n)!$ for any $n\in\mathbb{Z}_{\geq0}.$
136700
Proving divisibility of expression using induction
2554
Show that if $n>2$, then $(n!)^2>n^n$.
22073
Prove by induction that $n^2<n!$
4991
Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$
13330
Inductive Proof that $k!<k^k$, for $k\geq 2$.
91197
Proving $n! \ge 2^{n-1 }$for all $n\ge1 $by mathematical Induction
30783
Prove inequality $n<3^n$ using mathematical induction
49299
Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
66358
Prove by mathematical induction that $2n ≤ 2^n$, for all integer $n≥1$?
134000
Proof by Strong Induction: $n = 2^a b,\, b\,$ odd, every natural a product of an odd and a power of 2
55273
Prove by mathematical induction that: $\forall n \in \mathbb{N}: 3^{n} > n^{3}$
6165
Proof by Induction $n^2+n$ is even
11867
Prove by induction that $n < 2^n$ for all $n \ge 1$
52113
Proof by Induction $\sum_{i=0}^{k-1} 2^i = 2^k-1$