Prove that for every natural number greater than or equal to 6, (n+1)^2 is less than or equal to 2^n

Let S = {n in N s.t. n>=6, (n+1)^2 <= 2^n }

Show 6 is in S 7^2 <= 2^7

Assume n is in S

Show n+1 is in S

(n+2)^2 <= 2^n +1

n^2 + 4n + 4 <= 2^n +1 HELP!