Use mathematical induction to prove the following.7n > 7n-1
What will be an ideal response?
Answers may vary. One possibility:
Sn: 7n > 7n-1
S1: 71 > 71-1
Sk: 7k > 7k-1
Sk+1: 7k+1 > 7k
1. Basis step: Since 71-1 = 70 = 1 and 71 > 1, S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
7k > 7k-1
7k ? 7 > 7k-1 ? 7 Multiplying by 7, 7 > 0
7k+1 > 7(k-1)+1
7k+1 > 7k
Mathematics
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