Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 5 - Section 5.4 - Recursive Algorithms - Exercises - Page 371: 21

Answer

--Proving The algorithm for computing nx whenever n is a positive integer and x is an integer, using just addition.

Work Step by Step

--If n = 1, - then -nx = x, and the algorithm correctly returns x. - Assume that the algorithm correctly computes kx. To compute (k + 1)x -it recursively - computes the product of k + 1 − 1 = k and x, and then adds x. -- By the inductive hypothesis, -it computes that product correctly, so the answer returned is kx+x = (k+1)x, which is correct.
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