Use mathematical induction to prove the following.6n > 6n-1
What will be an ideal response?
Answers may vary. One possibility:
Sn: 6n > 6n-1
S1: 61 > 61-1
Sk: 6k > 6k-1
Sk+1: 6k+1 > 6k
1. Basis step: Since 61-1 = 60 = 1 and 61 > 1, S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
6k > 6k-1
6k ? 6 > 6k-1 ? 6 Multiplying by 6, 6 > 0
6k+1 > 6(k-1)+1
6k+1 > 6k
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