Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 5 - Sequences, Mathematical Induction, and Recursion - Exercise Set 5.7 - Page 315: 4

Answer

bk = 1/(k+1)

Work Step by Step

bk = bk-1/(1+bk-1), for all integers k ≥ 1, b0 = 1 b1 = b0/(1+b0) = 1/(1+1) = 1/2 b2 = b1/(1+b1) = (1/2)/(1+(1/2)) = 1/2/(3/2) = 1/2 * 2/3 = 1/3 b3 = b2/(1+b2) = (1/3)/(1+(1/3)) = 1/3/(4/3) = 1/3 * 3/4 = 1/4 b4 = b3/(1+b3) = 1/4/(1+(1/4)) = 1/4/(5/4) = 1/4*4/5 = 1/5 bk = 1/(k+1)
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