Q. 6 Express 1-12+13-14+15..........+... [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. 6 (page 838)

Express $1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} . . . . . . . . . . + \frac{1}{13}$ using summation notation.

Short Answer

Expert verified

The summation notation is: ${鈭�}_{n = 1}^{13} {(- 1)}^{n + 1} (\frac{1}{n})$ , where $n$ is positive integers.

Step by step solution

Step 1. Given information:

Series is : $1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + . . . . . . . . . . . + \frac{1}{13}$

Step 2. To find the general term of the series.

$1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + . . . . . . + \frac{1}{13} = {(- 1)}^{2} . \frac{1}{1} + {(- 1)}^{3} . \frac{1}{2} + {(- 1)}^{4} . (\frac{1}{3}) + {(- 1)}^{5} . (\frac{1}{4}) + . . . . . . . + {(- 1)}^{14} . (\frac{1}{13}) = {(- 1)}^{(1 + 1)} . \frac{1}{1} + {(- 1)}^{(2 + 1)} . \frac{1}{2} + {(- 1)}^{(3 + 1)} . (\frac{1}{3}) + {(- 1)}^{(4 + 1)} . (\frac{1}{4}) + . . . . . . . + {(- 1)}^{(13 + 1)} . (\frac{1}{13})$

From above expansion it is clear that the general term of the series can be written as

$a_{n} = {(- 1)}^{n + 1} . (\frac{1}{n})$ , where $n$ is positive integers.

Step 3. To write the series as summation notation.

Apply the limits $n = 1$ to $n = 13$ .

So summation notation is ${鈭�}_{n = 1}^{13} a_{n} = {鈭�}_{n = 1}^{13} {(- 1)}^{n + 1} . (\frac{1}{n})$

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91影视

Express $1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} . . . . . . . . . . + \frac{1}{13}$ using summation notation.

Short Answer

Step by step solution

Step 1. Given information:

Step 2. To find the general term of the series.

Step 3. To write the series as summation notation.

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91影视

Express 1-12+13-14+15..........+113using summation notation.

Short Answer

Step by step solution

Step 1. Given information:

Step 2. To find the general term of the series.

Step 3. To write the series as summation notation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Express $1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} . . . . . . . . . . + \frac{1}{13}$ using summation notation.