Chapter 12: Q 65. (page 809)

In Problems 61–70, express each sum using summation notation.
$1 - \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + . . . . . . + {(- 1)}^{6} \frac{1}{3^{6}}$

Short Answer

Expert verified

The required summation notation is $1 - \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + . . . . . . + {(- 1)}^{6} \frac{1}{3^{6}} = \sum_{k = 0}^{6} {(- 1)}^{k} \cdot (\frac{1}{3^{k}})$ .

Step by step solution

Step 1. Write the given information.

The given sum is:

1 - \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + . . . . . . + {(- 1)}^{6} \frac{1}{3^{6}}

Step 2. Write the sum using summation notation.

As we can see that the sum $1 - \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + . . . . . . + {(- 1)}^{6} \frac{1}{3^{6}}$ has 7 terms, each term represents the form ${(- 1)}^{k} (\frac{1}{3^{k}})$ , and starts at role="math" localid="1646761402358" $k = 0$ and ends at $k = 6$ .

Therefore,role="math" localid="1646761496603" $1 - \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + . . . . . . + {(- 1)}^{6} \frac{1}{3^{6}} = \sum_{k = 0}^{6} {(- 1)}^{k} \cdot (\frac{1}{3^{k}})$

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In Problems 61–70, express each sum using summation notation.
$1 - \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + . . . . . . + {(- 1)}^{6} \frac{1}{3^{6}}$

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Write the sum using summation notation.

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In Problems 61–70, express each sum using summation notation.1-13+19-127+......+-16136

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Write the sum using summation notation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Discrete Mathematics

Mechanics Maths

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

In Problems 61–70, express each sum using summation notation.
$1 - \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + . . . . . . + {(- 1)}^{6} \frac{1}{3^{6}}$