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Chapter 13: Q. 24 (page 1004)

Evaluate the sums in Exercises 23–28.
$\sum_{j = 1}^{3} \sum_{k = 1}^{2} k^{j}$

Short Answer

Expert verified

The value of summation is $17$

Step by step solution

01

Step 1. Given information

An expression is given as $\sum_{j = 1}^{3} \sum_{k = 1}^{2} k^{j}$

02

Step 2. Evaluating summation

First separate out the terms then simplify,

$\sum_{j = 1}^{3} \sum_{k = 1}^{2} k^{j} = \sum_{j = 1}^{3} (\sum_{k = 1}^{2} k^{j}) \sum_{k = 1}^{2} k^{j} = 1^{j} + 2^{j} \Rightarrow (1^{1} + 2^{1}) + (1^{2} + 2^{2}) + (1^{3} + 2^{3}) = 1 + 2 + 1 + 4 + 1 + 8 = 17$

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Most popular questions from this chapter

Discuss the similarities and differences between the definition of the definite integral found in Chapter 4 and the definition of the double integral found in this section.

What is the difference between a triple integral and an iterated triple integral?

Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.

$\int_{0}^{2} \int_{0}^{1 - 3 x / 2} \int_{2 x + (4 / 3) y - 4}^{0} f (x, y, z) d z d y d x$

$How many summands are in \sum_{j = 3}^{13} \sum_{k = 5}^{20} \frac{j^{2}}{e^{jk}} ?$

In Exercises 45–52, rewrite the indicated integral with the specified order of integration.

Exercise 41 with the order dy dx dz.

See all solutions

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