Use mathematical induction to prove the following.(46)n = 46n
What will be an ideal response?
Answers may vary. One possibility:
Sn: (46)n = 46n
S1: (46)1 = 46?1
Sk: (46)k = 46k
Sk+1: (46)k+1 = 46(k+1)
1. Basis step: Since 46?1 = 46 = (46)1, S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
(46)k = 46k
(46)k(46) = 46k(46)
(46)k+1 = 46k+6
(46)k+1 = 46(k+1).
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