Induction proof...I'm stuck!
Hopefully someone can help me with this..I'm nearly done.
I'm in the induction step of the proof & here's what I have:
"So suppose that P(n) holds for n an integer and n>=5, we have that
2^n > n^2.
We wish to show that P(n+1) holds, that is that
2^(n+1) > (n+1)^2. This can be rewritten as
2(2^n) > n^2 +2n +1.
So, by our induction hypothesis and our Lemma (stated & proved earlier before this proof) we have
2(2^n) > 2^n > n^2 > 2n+1."
....This is where I'm stuck...is there a property that allows me to then just state "Thus 2(2^n) > n^2 +2n +1"?
Thanx for any feedback you provide!