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 5.1 - Page 244: 78

Answer

See below.

Work Step by Step

By definition, we have: $LHS=\binom n {r+1}=\frac{n!}{(n-r-1)!(r+1)!}$ $RHS=\frac{n-r}{r+1}\binom n {r}=\frac{n-r}{r+1}\times\frac{n!}{(n-r)!(r)!}=\frac{n!}{(n-r-1)!(r+1)!}=LHS$
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