   Chapter 13.6, Problem 58E ### 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

# 58. DISCOVER PROVE: Sums of Binomial Coefficients Add each of the first five rows of Pascal’s Triangle, as indicated. Do you see a pattern?1+1=?1+2+1=?1+3+3+1=?1+4+6+4+1=?1+5+10+10+5+1=?On the basis of the patterns you have found, find the sum off the nth row: C n 0 + C n 1 + C n 2 + ⋅ ⋅ ⋅ + C n n Prove your result by expanding ( 1 + 1 ) n using the Binomial Theorem.

To determine

To find:

The sum of the nth row.

Explanation

Given:

1+1=?1+2+1=?1+3+3+1=?1+4+6+4+1=?1+5+10+10+5+1=?

Approach:

The binomial expansion of (1+1)n is given by

(1+1)n=Cn01n10+Cn11n111+Cn21n212++Cnn101n

Calculation:

1+1=21+2+1=41+3+3+1=81+4+6+4+1=161+5+10+10+5+1=32

Here, the pattern is 2n or (1+1)n where n is the row.

Now,

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 