   Chapter 13.6, Problem 53E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# Proving an Identity In this exercise we prove the identity ( n r − 1 ) + ( n r ) = ( n + 1 r ) (a) Write the left hand side of this equation as the sum of two fractions.(b) Show that a common denominator of the expression that you found in part (a) is r ! ( n − r + 1 ) ! (c) Add the two fractions using the common denominator in part (b), simplify the numerator, and note that the right-hand side of the equation.

To determine

a)

To show:

The left hand side of the equation is a sum of fractions.

Explanation

Approach:

Cnr=n!r!(nr)!

Calculation:

(nr1)+(nr)=Cnr1+Cn

To determine

b)

To show:

The common denominator of the expression is r!(nr+1)!.

To determine

c)

To show:

Cnr1+Cnr=Cnr+1

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