Use mathematical induction to prove that the statement is true for every positive integer n.6n > 6n-1

Question

What will be an ideal response?

Answer 1

Answers will vary. One possible proof follows.
a). Let n = 1. then, 61 = 6 > 61-1 = 60 = 1. So, the statement is true for n = 1.
b). Assume that the statement is true for n = k:
 6k > 6k-1
 Multiply both sides by 6:
 6?6k = 6k+1 > 6?6k-1 = 6k = 6(k+1)-1 or 6k+1 > 6(k+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.