Chapter 4: Q. 42 (page 326)

Write each expression in Exercises 41–43 in one sigma notation (with some extra terms added to or subtracted from the sum, as necessary).
$\sum_{k = 1}^{40} \frac{1}{k} - \sum_{k = 0}^{39} \frac{1}{k + 1}$

Short Answer

Expert verified

One sigma notation is : $\sum_{k = 1}^{39} (\frac{1}{k} - \frac{1}{k + 1}) - \frac{39}{40}$

Step by step solution

Step 1. Given information

Expression in sigma notation:

$\sum_{k = 1}^{40} \frac{1}{k} - \sum_{k = 0}^{39} \frac{1}{k + 1}$

Step 2. Write expression into one sigma notation:

$\sum_{k = 1}^{39} \frac{1}{k} - \sum_{k = 0}^{39} \frac{1}{k + 1} = (\sum_{k = 1}^{39} \frac{1}{k} + \frac{1}{40}) - (\frac{1}{0 + 1} {+ \sum}_{k = 1}^{39} \frac{1}{k + 1}) = \sum_{k = 1}^{39} \frac{1}{k} + \frac{1}{40} - 1 - \sum_{k = 1}^{39} \frac{1}{k + 1} = \sum_{k = 1}^{39} (\frac{1}{k} - \frac{1}{k + 1}) + \frac{1 - 40}{40} = \sum_{k = 1}^{39} (\frac{1}{k} - \frac{1}{k + 1}) - \frac{39}{40}$

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.

Write each expression in Exercises 41–43 in one sigma notation (with some extra terms added to or subtracted from the sum, as necessary).
$\sum_{k = 1}^{40} \frac{1}{k} - \sum_{k = 0}^{39} \frac{1}{k + 1}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write expression into one sigma notation:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Decision Maths

Applied Mathematics

Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

Write each expression in Exercises 41–43 in one sigma notation (with some extra terms added to or subtracted from the sum, as necessary).∑k=1401k-∑k=0391k+1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write expression into one sigma notation:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Decision Maths

Applied Mathematics

Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

Write each expression in Exercises 41–43 in one sigma notation (with some extra terms added to or subtracted from the sum, as necessary).
$\sum_{k = 1}^{40} \frac{1}{k} - \sum_{k = 0}^{39} \frac{1}{k + 1}$