Chapter 11.4, Problem 42E

Some statements arc false for the first fete positive integers, but true for some positive integer m on. In these instances, you can prove $S_n$ for $n\ge m$ by showing that $S_n$ is true and that $S_k$ implies $S_{k-1}$ when $k\ge m$

, Use this extended principle of mathematical induction to prove that each statement in Exercises 41-12 is true.

Prove that $2^n>n^2$ for $n\ge 5$, Show that the formula is true for $n=5$ and then use step 2 of mathematical induction.