/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 23 In Problems 22鈥�25, determine w... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Q. 23 (page 838)

In Problems 22鈥�25, determine whether each infinite geometric series converges or diverges. If it converges, find its sum

2-1+12-14+.....

Short Answer

Expert verified

The geometric series converges.

Its sum is:43

Step by step solution

01

Step 1. Given information.

The series is :

2-1+12-14+.....
02

Step 2. To find common ratio and first term. 

First term of the series is:a=2

Common ratio is:

r=-12

r=12

Sincer<1

Hence given series converges.

03

Step 3. To find sum of infinite terms. 

S鈭�=21--12=21+12=232=43

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A pond currently has 2000 trout in it. A fish hatchery decides to add an additional 20 trout each month. In addition, it is known that the trout population is growing 3% per month. The size of the population after n months is given by the recursively defined sequence.

p0=2000;pn=1.03pn-1+20

(a) How many trout are in the pond at the end of the second month? That is, what is p2?

(b) Using a graphing utility, determine how long it will be

before the trout population reaches 5000.

In Problems 71-82, find the sum of each sequence.

鈭�k=840(-3k)

In Problems 51鈥�60, write out each sum.

鈭�k=0n13k

In Problems 29鈥�36, the given pattern continues. Write down the nth term of a sequence ansuggested by the pattern.

2,-4,6,-8,10,...

In Problems 37鈥�50, a sequence is defined recursively. Write down the first five terms.

a1=2;an=2+an-1
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.