Let S(n) = 1 + 2 +???..+ n be the sum of the first n natural numbers and let C(n) =13 + 23 + -
Let S(n) = 1 + 2 +???..+ n be the sum of the first n natural numbers and let C(n) =13 + 23 + - + n3 be the sum of the first n cubes. Prove the following equalities by induction on n, to arrive at the curious conclusion that C(n) = S 2 (n) for every n.
a.
b.
S(n) = n(n+1). C(n) = (n + 2n + n) = n(n + 1)
Step by Step Solution
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Step: 1
a The sum of the first n natural numbers S n 1 2 3 n is given by Hence induction method is us...
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Step: 2
Step: 3
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Authors: Allen R. Angel, Christine D. Abbott, Dennis Runde
10th edition
134112105, 134112342, 9780134112343, 9780134112268, 134112261, 978-0134112107
