Chapter 7: Q 60. (page 615)

Determine whether the series $\frac{99}{40} - \frac{99}{20} + \frac{99}{10} - \frac{99}{5} + \dots$ converges or diverges. Give the sum of the convergent series.

Short Answer

Expert verified

The series $\frac{99}{40} - \frac{99}{20} + \frac{99}{10} - \frac{99}{5} + \dots$ diverges.

Step by step solution

Step 1. Given information.

Given a series $\frac{99}{40} - \frac{99}{20} + \frac{99}{10} - \frac{99}{5} + \dots$ .

Step 2. Find if the series converges or not.

The standard form of a geometric series is $\sum_{k = 0}^{\infty} c r^{k}$ .

The geometric series converges if and only if $|r| < 1$ .

In the series role="math" localid="1648983721211" $\frac{99}{40} - \frac{99}{20} + \frac{99}{10} - \frac{99}{5} + \dots$ it can be seen that $c = \frac{99}{40}$ .

Every term after that is $- 2$ times the previous term.

It follows that $r = - 2$ .

Since $r = - 2$ , the series $\frac{99}{40} - \frac{99}{20} + \frac{99}{10} - \frac{99}{5} + \dots$ diverges.

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Determine whether the series $\frac{99}{40} - \frac{99}{20} + \frac{99}{10} - \frac{99}{5} + \dots$ converges or diverges. Give the sum of the convergent series.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find if the series converges or not.

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Determine whether the series 9940-9920+9910-995+…converges or diverges. Give the sum of the convergent series.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find if the series converges or not.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Determine whether the series $\frac{99}{40} - \frac{99}{20} + \frac{99}{10} - \frac{99}{5} + \dots$ converges or diverges. Give the sum of the convergent series.