Copy the steps below and fill in the blanks to prove that n ! > 2ⁿ for n ≥ 4. Note that we do not start with n = 1. Verify that the statement is false for n < 4. Homework Help ✎

1. Verify the statement is true for n = 4.

2. Assume the statement is true for n = k.

3. Prove the statement is true for n = k + 1.

   Recall that: (k + 1)! = ____ (k + 1)

   We assumed that k ! > 2^k , therefore (k + 1)! = ____ (k + 1) > ____ (k + 1).

   Because k ≥ 4, k + 1 > 2 and hence ____ (k + 1) > 2^k · ____ = 2−.

   Following the steps from above, we have shown that ____ > ____.

4. Write a conclusion for your proof by induction.