Prove by induction that $2^n\le (n+1)!$ for all $n\in\Bbb N$.
61117
Prove by induction: $n! \ge 2^{(n-1)}$ for any $n \ge 1$
88144
Induction Proof $n! < n^n$
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
55266
Prove that $(n+1)^{n-1}<n^n$
130093
Prove by Induction : $n < 2^n$
145519
Prove that for any natural number $n>1$, we have $(2n)!<(n(n+1))^n$
55273
Prove by mathematical induction that: $\forall n \in \mathbb{N}: 3^{n} > n^{3}$
79652
Proof by induction that $2 + 4 + 6 + \cdots + 2n = n(n+1)$
153123
Proving by induction $4^n  0$
78726
Prove via mathematical induction that $4n < 2^n$ for all $ n≥5$.
69921
Prove that: $(1+a_1)(1+a_2)...(1+a_n) \le 1 + S_n + (S_n)^2/2! + ... + (S_n)^n/n!$
85731
Prove by induction that $n! > n^2$
87941
Prove by mathematical induction that $\forall n \in \mathbb{N} : \sum_{k=1}^{2n} \frac{(-1)^{k+1}}{k} = \sum_{k=n+1}^{2n} \frac{1}{k} $
124240
Inductive proof of $\,9 \mathrel| 4^n+6n-1\,$ for all $\,n\in\Bbb N$
3043
Prove $n!>2^n$ for $n\geq4$ using induction.