Chapter 13: Q. 25 (page 1004)

Evaluate the sums in Exercises $23 - 28$ .
$\sum_{j = 1}^{3} \sum_{k = 1}^{4} (3 j - 4 k)$

Short Answer

Expert verified

The value of the summation is $- 48$

Step by step solution

Step 1. Given information

An expression is given as $\sum_{j = 1}^{3} \sum_{k = 1}^{4} (3 j - 4 k)$

Step 2. Evaluating summation

First separate out the term and then simplify,

$\sum_{j = 1}^{3} \sum_{i = 1}^{4} (3 j - 4 k) = \sum_{j = 1}^{3} (\sum_{k = 1}^{4} (3 j - 4 k)) \sum_{k = 1}^{4} (3 j - 4 k) = (3 j - 4 \times 1) + (3 j - 4 \times 2) + (3 j - 4 \times 3) + (3 j - 4 \times n) = 12 j - 4 \times (1 + 2 + 3 + 4) = 12 j - 4 \times 10 = 12 j - 40 \sum_{j = 1}^{3} \sum_{k = 1}^{4} (3 j - 4 k) = \sum_{j = 1}^{3} (\sum_{k = 1}^{4} (3 j - 4 k)) = \sum_{j = 1}^{3} (12 j - 40) = (12 \times 1 - 40) + (12 \times 2 - 40) + (12 \times 3 - 40) = 12 (1 + 2 + 3) - 3 \times 40 = 12 \times 6 - 120 = 72 - 120 = - 48$

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.

Evaluate the sums in Exercises $23 - 28$ .
$\sum_{j = 1}^{3} \sum_{k = 1}^{4} (3 j - 4 k)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluating summation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Logic and Functions

Pure Maths

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

Evaluate the sums in Exercises 23–28.∑j=13∑k=14(3j-4k)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluating summation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Logic and Functions

Pure Maths

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

Evaluate the sums in Exercises $23 - 28$ .
$\sum_{j = 1}^{3} \sum_{k = 1}^{4} (3 j - 4 k)$