Use mathematical induction to prove the following.(35)n = 35n
What will be an ideal response?
Answers may vary. One possibility:
Sn: (35)n = 35n
S1: (35)1 = 35?1
Sk: (35)k = 35k
Sk+1: (35)k+1 = 35(k+1)
1. Basis step: Since 35?1 = 35 = (35)1, S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
(35)k = 35k
(35)k(35) = 35k(35)
(35)k+1 = 35k+5
(35)k+1 = 35(k+1).
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