Prove 2n n for all positive integers nSolutionWe can prove

Prove 2^n > n for all positive integers n.

We can prove that 2^n > n for all positive integers n by induction.

First for n = 1, 2^n = 2 which is greater than 1.

Assume 2^n > n

Now 2^(n + 1) should be greater than (n + 1)

2^(n + 1) = 2*2^n > 2n

2n = n + n > n + 1

=> 2^(n + 1) > n + 1 if 2^n > n

This proves that 2^n > n for all positive integers n.