1. The problem statement, all variables and given/known data Using the principle of mathematical induction, prove that for all n>=10, 2^n>n^3 2. Relevant equations 2^(n+1) = 2(2^n) (n+1)^3 = n^3 + 3n^2 + 3n +1 3. The attempt at a solution i) (Base case) Statement is true for n=10 ii)(inductive step) Suppose 2^n > n^3 for some integer >= 10 (show that 2^(n+1) > (n+1)^3 ) Consider 2^(n+1). 2^(n+1)= 2(2^n) > 2(n^3) = n^3 + n^3 (Ok, so this is where i'm stuck. Can I say n^3 > 3n^2 + 3n +1 because n>=10? Because if I can say that, then I can proceed with n^3 + n^3 > n^3 + 3n^2 + 3n +1 = (n+1)^3. I just don't know if i have to further justify it. Should I do another proof by induction to show that n^3 > 3n^2 + 3n +1 for n>=10? Or can I make a general statement that the power of 3 is higher than a power of 2 and so on) Thank you!