Chapter 12: Q 70. (page 809)

In Problems 61–70, express each sum using summation notation.
$a + a r + a r^{2} + . . . . . + a r^{n - 1}$

Short Answer

Expert verified

The required summation notation is $a + a r + a r^{2} + . . . . . + a r^{n - 1} = \sum_{k = 1}^{n} a r^{k - 1}$ .

Step by step solution

Step 1. Write the given information.

The given sum is:

$a + a r + a r^{2} + . . . . . + a r^{n - 1}$

Step 2. Write the sum using summation notation.

Write each term in the same format:

$a + a r + a r^{2} + . . . . . + a r^{n - 1} = a {(r)}^{0} + a {(r)}^{1} + a {(r)}^{2} + . . . . . + a {(r)}^{n - 1} = a {(r)}^{1 - 1} + a {(r)}^{2 - 1} + a {(r)}^{3 - 1} + . . . . . . + a {(r)}^{n - 1} = \sum_{k = 1}^{n} a r^{k - 1}$

Therefore, localid="1646799831123" $a + a r + a r^{2} + . . . . . + a r^{n - 1} = \sum_{k = 1}^{n} a r^{k - 1}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Problems 61–70, express each sum using summation notation.
$a + a r + a r^{2} + . . . . . + a r^{n - 1}$

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Write the sum using summation notation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Calculus

Decision Maths

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 61–70, express each sum using summation notation.a+ar+ar2+.....+arn-1

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Write the sum using summation notation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Calculus

Decision Maths

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 61–70, express each sum using summation notation.
$a + a r + a r^{2} + . . . . . + a r^{n - 1}$