Prove by induction that $n! > n^2$
22073
Prove by induction that $n^2<n!$
2554
Show that if $n>2$, then $(n!)^2>n^n$.
10604
Prove $3^n > n^2$ by induction
40692
Proving by strong induction that $\forall n \ge 2, \;\forall d \ge 2 : d \mid n(n+1)(n+2)...(n+d-1) $
44864
Prove, formally that: $\log_2 n! \ge n$ , for all integers $n>3$.
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
79145
Proving by induction: $2^n > n^3 $ for any natural number $n > 9$
3043
Prove $n!>2^n$ for $n\geq4$ using induction.
139269
Prove that $2n-3\leq 2^{n-2}$ , for all $n \geq 5$ by mathematical induction
100558
Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
17047
Prove that if n is even then $n^2$ is even and if n is odd then $n^2$ is odd?
120093
Proof of inequality $2(\sqrt{n+1}-\sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n} - \sqrt{n-1})$ using induction
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
96332
Prove by induction that $\sqrt[n+1]{n+1}<\sqrt[n]{n}$ for $n\ge 3$
15838
Induction Proof that $x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1})$
16798
Prove the inequality $n! \geq 2^n$ by induction
105854
Prove $n^2(n^4-1)$ is divisible by 60 using Mathematical Induction.