Use mathematical induction to prove that the statement is true for every positive integer n.4n > 1

Question

What will be an ideal response?

Answer 1

Answers will vary. One possible proof follows.
a). Let n = 1. Then, 91 = 9 > 1, so the statement is true for n = 1.
b). Assume the statement is true for n = k:
 9k > 1
 Multiply both sides by 9:
 9?9k = 9k+1 > 1?9 = 9 or 9k+1 > 9. Also, 9 > 1, so 9k+1 > 1.
Since the statement is true for n = k + 1 as long as it is true for n = k, and since the statement is true for n = 1, then it is true for all natural numbers n.