$\forall n \geq 5$ prove $2^n > n^2$
135614
Show that $2^n > n^2$ whenever n>4.
4970
For $n \geq 2$, show that $n \nmid 2^{n}-1$
33757
For what natural numbers is $n^3 < 2^n$? Prove by induction
149216
Give a combinatorial proof to show the following for all integers $n \geq 2$.
66387
Prove $(x_1+.....+x_n)^2 \leq n(x_1^2 + .....+x_n^2)$
72600
Proof that $n!\leq {(\frac{n+1}{2})}^{n}$
10604
Prove $3^n > n^2$ by induction
85731
Prove by induction that $n! > n^2$
78190
How to prove that for all natural numbers, $4^n > n^3$?
99052
Prove that $( 1 + n^{-2}) ^n \to 1$.
23684
Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime
26514
Prove that if $n$ is a composite, then $2^n-1$ is composite.
70926
Showing that for $n\geq 3$ the inequality $(n+1)^n<n^{(n+1)}$ holds
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
2197
Induction principle for $n!<n^n$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$