Use mathematical induction to prove the following.8n > n
What will be an ideal response?
Answers may vary. One possibility:
Sn: 8n > n
S1: 81 > 1
Sk: 8k > k
Sk+1: 8k+1 > k + 1
Step 1: Since 81 > 1, S1 is true.
Step 2: Let k be any natural number. Assume Sk. Deduce Sk+1.
8k > k
8k8 > k8 Multiplying by 8, 8 > 0
8k+1 > k(1 + 7)
8k+1 > k + 7k
7k ? 1 7 ? 1 and k ? 1
8k+1 > k + 1
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