# Math Help - induction problem

1. ## induction problem

i think this one is pretty easy but i'm not that great with induction. any help?

Show that $2^n > n$ for any integer n that is an element of $Z^+.$

my attempt:

base case - let n=1
2^1=2 > 1 -> base case is true

2^(n+1) > n+1
2^n + 2 > n+1
2^n > n-1

statement holds true by the base case 2^1 > 1-1

2. For n=1, $2^{1} = 2 > 1$.

Now Assume $2^{k} > k$ for some k>1

then $2^{k+1} = 2*2^{k} > 2k$ by the induction step

and $2k = k+k > k+1$ which is what we wanted to show