Question Detail
Question
Prove by induction that n! > 2^n for n > 4.
Correct Answer
Option A is the correct answer.
Detailed Explanation
Base case n=5: 5! = 120 > 2^5 =32 ✔. Assume n=k: k!>2^k. For n=k+1: (k+1)! = (k+1)×k! > (k+1)×2^k > 2×2^k=2^{k+1} ✔ since k+1>2 for k>4.
Hint
Multiply inequality by (k+1) and compare with 2^(k+1).