Use mathematical induction to prove the following.(34)n = 34n
What will be an ideal response?
Answers may vary. One possibility:
Sn: (34)n = 34n
S1: (34)1 = 34?1
Sk: (34)k = 34k
Sk+1: (34)k+1 = 34(k+1)
1. Basis step: Since 34?1 = 34 = (34)1, S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
(34)k = 34k
(34)k(34) = 34k(34)
(34)k+1 = 34k+4
(34)k+1 = 34(k+1).
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