Use mathematical induction to prove the following.9n > 9n-1
What will be an ideal response?
Answers may vary. One possibility:
Sn: 9n > 9n-1
S1: 91 > 91-1
Sk: 9k > 9k-1
Sk+1: 9k+1 > 9k
Step 1: Since 91-1 = 90 = 1 and 91 > 1, S1 is true.
Step 2: Let k be any natural number. Assume Sk. Deduce Sk+1.
9k > 9k-1
9k9 > 9k-19 Multiplying by 9, 9 > 0
9k+1 > 9(k-1)+1
9k+1 > 9k
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