Use mathematical induction to prove that the statement is true for every positive integer n.4n > 1
What will be an ideal response?
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.
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