Some statements are false for the first few positive integers, but true for some positive integer m on. In these instances, you can prove Sn for n ≥ m by showing that S_m is true and that S_k implies S_k+1 when k ≥ m. Use this extended principle of mathematical induction to prove that each statement in Exercises 41–42 is true.

Prove that 2ⁿ > n² for n ≥ 5. Show that the formula is true for n = 5 and then use step 2 of mathematical induction.