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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

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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Chapter 13 Solutions

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