Chapter 12: Q. 324 (page 1222)

Write the following using summation notation. $- 1 + \frac{1}{4} - \frac{1}{9} + \frac{1}{16} - \frac{1}{25}$

Short Answer

Expert verified

The summation notation for the sequence $- 1 + \frac{1}{4} - \frac{1}{9} + \frac{1}{16} - \frac{1}{25}$ is $\sum_{n = 1}^{5} \frac{{(- 1)}^{n}}{n^{2}}$

Step by step solution

Step 1. Given

The expression $- 1 + \frac{1}{4} - \frac{1}{9} + \frac{1}{16} - \frac{1}{25}$

To write the expression using sum notation.

Step 2. Look for the pattern in the term

The number of terms are $n = 1, 2, 3, 4, 5$ and the pattern will be like,

$- \frac{1}{1^{2}}, \frac{1}{2^{2}}, - \frac{1}{3^{2}}, \frac{1}{4^{2}}, - \frac{1}{5^{2}}$

Step 3. Write with summation notation

From the pattern, the numerator is the alternative negative sign while the denominator is the square of numbers from $1$ to $5$ .

So the summation notation is,

$- 1 + \frac{1}{4} - \frac{1}{9} + \frac{1}{16} - \frac{1}{25} = \sum_{n = 1}^{5} \frac{{(- 1)}^{n}}{n^{2}}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Write the following using summation notation. $- 1 + \frac{1}{4} - \frac{1}{9} + \frac{1}{16} - \frac{1}{25}$

Short Answer

Step by step solution

Step 1. Given

Step 2. Look for the pattern in the term

Step 3. Write with summation notation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Applied Mathematics

Theoretical and Mathematical Physics

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Write the following using summation notation. -1+14-19+116-125

Short Answer

Step by step solution

Step 1. Given

Step 2. Look for the pattern in the term

Step 3. Write with summation notation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Applied Mathematics

Theoretical and Mathematical Physics

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Write the following using summation notation. $- 1 + \frac{1}{4} - \frac{1}{9} + \frac{1}{16} - \frac{1}{25}$