Use mathematical induction to prove the following.(69)n = 69n
What will be an ideal response?
Answers may vary. One possibility:
Sn: (69)n = 69n
S1: (69)1 = 69?1
Sk: (69)k = 69k
Sk+1: (69)k+1 = 69(k+1)
1. Basis step: Since 69?1 = 69 = (69)1, S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
(69)k = 69k
(69)k(69) = 69k(69)
(69)k+1 = 69k+9
(69)k+1 = 69(k+1).
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