Chapter 12: Q. 257 (page 1218)

In the following exercises, write each sum using summation notation.
$- \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + \frac{1}{81} - \frac{1}{243}$

Short Answer

Expert verified

The summation notation is $\sum_{n = 1}^{5} {(- 1)}^{n} \frac{1}{3^{n}}$ .

Step by step solution

Step 1. Given information.

The given expression is,

$- \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + \frac{1}{81} - \frac{1}{243}$ .

Step 2. Finding the summation notation.

Here, the numerators are all one's and the denominators are $3$ power from $1$ to $5$ with alternative signs then we get,

localid="1645358215087" $- \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + \frac{1}{81} - \frac{1}{243} n : 1, 2, 3, 4, 5 T e r m s : - \frac{1}{3}, \frac{1}{9}, - \frac{1}{27}, \frac{1}{81}, - \frac{1}{243} P a t t e r n : {(- 1)}^{1} \frac{1}{3^{1}}, {(- 1)}^{2} \frac{1}{3^{2}}, {(- 1)}^{3} \frac{1}{3^{3}}, {(- 1)}^{4} \frac{1}{3^{4}}, {(- 1)}^{5} \frac{1}{3^{5}}, . . . . . . . . {(- 1)}^{n} \frac{1}{3^{n}}$

Then the sum can be written in the form of summation notation that is

$- \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + \frac{1}{81} - \frac{1}{243} = \sum_{n = 1}^{5} {(- 1)}^{n} \frac{1}{3^{n}}$ .

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In the following exercises, write each sum using summation notation.
$- \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + \frac{1}{81} - \frac{1}{243}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Finding the summation notation.

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In the following exercises, write each sum using summation notation.-13+19-127+181-1243

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Finding the summation notation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Discrete Mathematics

Statistics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, write each sum using summation notation.
$- \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + \frac{1}{81} - \frac{1}{243}$