Use mathematical induction to prove the following.3n > n

What will be an ideal response?


Answers may vary. One possibility:
Sn: 3n > n
S1: 31 > 1
Sk: 3k > k
Sk+1: 3k+1 > k + 1
1. Basis step: Since 31 > 1, S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
3k > k
3k ? 3 > k ? 3 Multiplying by 3, 3 > 0
3k+1 > k(1 + 2)
3k+1 > k + 2k
2k ? 1 2 ? 1 and k ? 1
3k+1 > k + 1

Mathematics

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