Thread: induction problem

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

Show that for any integer n that is an element of

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

For n=1, .

Now Assume for some k>1

then by the induction step

and which is what we wanted to show