Prove that $n<2^n$ for any natural number $n$.
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
125707
A simple proof (hopefully) for $2^x \neq 0$
139269
Prove that $2n-3\leq 2^{n-2}$ , for all $n \geq 5$ by mathematical induction
6165
Proof by Induction $n^2+n$ is even
140409
Prove that $\sqrt{n} > \ln n$
154475
Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number
88838
How can I prove this inequality for $n\geq 2$?
95061
Proving that $2^{2\cdot 3^{n-1}}\equiv 1+3^n\pmod{3^{n+1}}$ for every natural $n$
135018
Proving that a sequence has $a_n = a_{n+2}$ for $n$ sufficiently large.
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$
11867
Prove by induction that $n < 2^n$ for all $n \ge 1$
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
82774
Prove by mathematical induction that $n^3 - n$ is divisible by $3$ for all natural number $n$
88628
Proving the total number of subsets of S is equal to $2^n$
152577
Proving $4^n > n^4$ holds for $n\geq 5$ via induction.
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$