Use mathematical induction to prove the following.2n > 2n-1
What will be an ideal response?
Answers may vary. One possibility:
Sn: 2n > 2n-1
S1: 21 > 21-1
Sk: 2k > 2k-1
Sk+1: 2k+1 > 2k
1. Basis step: Since 21-1 = 20 = 1 and 21 > 1, S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
2k > 2k-1
2k ? 2 > 2k-1 ? 2 Multiplying by 2, 2 > 0
2k+1 > 2(k-1)+1
2k+1 > 2k
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