Hi there folks, I have just a small problem with a specific induction problem. The problem itself is: "Prove [tex]n! > 4^n[/tex], for all n >= 9." So here's my work: 1) Show true for n = 9 LS 9! = 362880 RS 4^9 = 262144 .:. LS > RS 2) Assume true for n = k i.e. Assume that k! > 4^k 3) Prove true for n = k+1 i.e. Prove that (k+1)! > 4^(k+1) So I begin to expand the LHS out (k+1)! = (k+1)(k)! > (K+1)(4^k) (by induction hypothesis) this is the problem that I encounter. I get stuck here because I don't exactly know how to followthrough at this point. How does (k+1)(4^k) become greater that 4^(k+1) ?