Prove by induction, for all positive integers $n$, that $n!\ge2^{n-1}$
61117
Prove by induction: $n! \ge 2^{(n-1)}$ for any $n \ge 1$
22073
Prove by induction that $n^2<n!$
87813
How to show that for all k, $k! \ge (k/2)^{k/2}$
121107
Proof by induction: $n^{n+1} > (n + 1)^n$, $(1 + x)^n \ge 1 + nx$, other inequalities
40692
Proving by strong induction that $\forall n \ge 2, \;\forall d \ge 2 : d \mid n(n+1)(n+2)...(n+d-1) $
119436
Proving $2^n\leq 2^{n+1}-2^{n-1}-1$ for all $n\geq 1$ by induction
57780
$\sum_{i=1}^n i\cdot i! = (n+1)!-1$ By Induction
138846
Prove by induction that $3\mid n^4-n^2$ for all $n \in \mathbb{Z^+}$, $n\ge2$.
4970
For $n \geq 2$, show that $n \nmid 2^{n}-1$
71650
Proving by strong induction for a sequence of integers, $2^n$ divides term $n$
70625
Prove By Induction $1 + 1/2 + 1/3 + ... + 1/(2^n) ≥ 1 + n/2$
8609
Prove by induction that $n!>2^n$
121544
Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
62177
Prove that: $2^n < n!$ Using Induction
14064
Proof by induction that $\sum_{i=1}^n \frac{i}{(i+1)!}=1- \frac{1}{(n+1)!}$
15838
Induction Proof that $x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1})$
6165
Proof by Induction $n^2+n$ is even