Use mathematical induction to prove the following.(48)n = 48n
What will be an ideal response?
Answers may vary. One possibility:
Sn: (48)n = 48n
S1: (48)1 = 48?1
Sk: (48)k = 48k
Sk+1: (48)k+1 = 48(k+1)
Step 1: Since 48?1 = 48 = (48)1, S1 is true.
Step 2: Let k be any natural number. Assume Sk. Deduce Sk+1.
(48)k = 48k
(48)k(48) = 48k(48)
(48)k+1 = 48k+8
(48)k+1 = 48(k+1).
Mathematics
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