Use mathematical induction to prove the following.7n > n
What will be an ideal response?
Answers may vary. One possibility:
Sn: 7n > n
S1: 71 > 1
Sk: 7k > k
Sk+1: 7k+1 > k + 1
Step 1: Since 71 > 1, S1 is true.
Step 2: Let k be any natural number. Assume Sk. Deduce Sk+1.
7k > k
7k7 > k7 Multiplying by 7, 7 > 0
7k+1 > k(1 + 6)
7k+1 > k + 6k
6k ? 1 6 ? 1 and k ? 1
7k+1 > k + 1
Mathematics
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