Use mathematical induction to prove the following.(67)n = 67n
What will be an ideal response?
Answers may vary. One possibility:
Sn: (67)n = 67n
S1: (67)1 = 67?1
Sk: (67)k = 67k
Sk+1: (67)k+1 = 67(k+1)
Step 1: Since 67?1 = 67 = (67)1, S1 is true.
Step 2: Let k be any natural number. Assume Sk. Deduce Sk+1.
(67)k = 67k
(67)k(67) = 67k(67)
(67)k+1 = 67k+7
(67)k+1 = 67(k+1).
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