   Chapter 13.6, Problem 54E ### 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

# 49-52 Proving a statement Show that the given statement is true.Prove that ( n r ) is an integer for all n and for 0 ≤ r ≤ n .[Suggestion: Use induction to show that the statement is true for all n, and use Exercise 53 for the induction step.]

To determine

To prove:

Cnr is an integer for all n and for 0rn.

Explanation

Given:

Cnr

Approach:

1. Cnr is an integer for n=1.

2. If Cnr is an integer for n=k, then Cnr is an integer for n=k+1 as well.

Here, n and r are positive integers.

Calculation:

Let P(n)= Cnr

For n=1

P(1)=C1r=1!r!(1r)!

Since n=1, then r=0 or r=1.

Thus, C1r is an integer.

The statement is true for n=1

Let the statement is true for n=k, then

P(k)= Ckr is an integer for k and for 0rk

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