Use mathematical induction to prove the following.0.11n < 0.11n-1
What will be an ideal response?
Answers may vary. One possibility:
Sn: 0.11n < 0.11n-1
S1: 0.111 < 0.111-1
Sk: 0.11k < 0.11k-1
Sk+1: 0.11k+1 < 0.11k
1. Basis step: Since 0.111-1 = 0.110 = 1 and 0.111 < 1, S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
0.11k < 0.11k-1
0.11k ? 0.11 < 0.11k-1 ? 0.11 Multiplying by 0.11, 0.11 > 0
0.11k+1 < 0.11(k-1)+1
0.11k+1 < 0.11k.
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