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 fornan integer andn>=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!