Q 65. In Problems 61鈥�70, express eac... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q 65. (page 809)

In Problems 61鈥�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 $1 - \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + . . . . . . + {(- 1)}^{6} \frac{1}{3^{6}} = {鈭�}_{k = 0}^{6} {(- 1)}^{k} 路 (\frac{1}{3^{k}})$ .

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" $1 - \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + . . . . . . + {(- 1)}^{6} \frac{1}{3^{6}} = {鈭�}_{k = 0}^{6} {(- 1)}^{k} 路 (\frac{1}{3^{k}})$

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91影视

In Problems 61鈥�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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91影视

In Problems 61鈥�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

Calculus

Mechanics Maths

Probability and Statistics

Pure Maths

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

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