Use mathematical induction to prove the following.0.19n < 0.19n-1
What will be an ideal response?
Answers may vary. One possibility:
Sn: 0.19n < 0.19n-1
S1: 0.191 < 0.191-1
Sk: 0.19k < 0.19k-1
Sk+1: 0.19k+1 < 0.19k
Step 1: Since 0.191-1 = 0.190 = 1 and 0.191 < 1, S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
0.19k < 0.19k-1
0.19k0.19 < 0.19k-10.19 Multiplying by 0.19, 0.19 > 0
0.19k+1 < 0.19(k-1)+1
0.19k+1 < 0.19k.
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