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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 12: Q 70 (page 1175)

In the following exercises, write each sum using summation notation.
$1 - 3 + 5 - 7 + 9 + \dots + 21$

Short Answer

Expert verified

The sum can be written as $Σ_{n = 1}^{11} {(- 1)}^{n + 1} (2 n - 1)$

Step by step solution

01

Step 1. Given information

$1 - 3 + 5 - 7 + 9 + \dots + 21$

02

Step 2. Write the sum

We look for a pattern in the terms

$1 - 3 + 5 - 7 + 9 + \dots + 21$

The signs of the terms alternate and the even terms are negative.

The sum written in summation notation is

localid="1646925610407" $Σ_{n = 1}^{11} {(- 1)}^{n + 1} (2 n - 1)$

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Most popular questions from this chapter

Find the coefficient of the $x^{4}$ term of $(x + 2)^{7}$ .

Write the first five terms of the sequence whose general term is $a_{n} = \frac{(n - 1)!}{(n + 1)!}$

In the following exercises, determine if each sequence is arithmetic, and if so, indicate the common difference.

$13, 9, 5, 1, - 3, - 7, . . . . .$

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.

$a_{1} = 9$ and $r = 2$

Find the eighteenth term of a sequence where the first term is 13 and the common difference is −7.

See all solutions

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