Use mathematical induction to prove the following.0.92n < 0.92n-1
What will be an ideal response?
Answers may vary. One possibility:
Sn: 0.92n < 0.92n-1
S1: 0.921 < 0.921-1
Sk: 0.92k < 0.92k-1
Sk+1: 0.92k+1 < 0.92k
1. Basis step: Since 0.921-1 = 0.920 = 1 and 0.921 < 1, S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
0.92k < 0.92k-1
0.92k ? 0.92 < 0.92k-1 ? 0.92 Multiplying by 0.92, 0.92 > 0
0.92k+1 < 0.92(k-1)+1
0.92k+1 < 0.92k.
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