Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 11.4, Problem 24PPS
To determine

To find the sum of the infinite series (if it exists):

  12+16+118+......

Expert Solution & Answer
Check Mark

Answer to Problem 24PPS

  0.52

Explanation of Solution

Given:

  12+16+118+......

Concept Used:

  1. Sum of an infinite series a+ar+ar2+ar3...... , whose first term is a and common ratio is r such that |r|<1is:
  2.   n=0arn=a1r

  3. Sum of an infinite series a+ar+ar2+ar3...... , whose first term is a and common ratio is r such that r>1 does not exist.

Calculation:

In order to find the sum of infinite series

  12+16+118+......

Use the formula

  n=0arn=a1r

Note from the given infinite series that first term is 12 , and the common ratio ( r ) can be find by dividing second term by first term, as

  r=a2a1

Since, here

  a2=16,a1=12

Thus,

  r=1612=16×21=13=0.33

Since, |r|<1 .

Thus, sum of given infinite series can be find using the formula

  n=0arn=a1r

As

  12+16+118+......=1210.33=0.50.96=0.52

Thus, the sum of the infinite series,

  12+16+118+......=0.52

Chapter 11 Solutions

Algebra 2

Ch. 11.1 - Prob. 1CYUCh. 11.1 - Prob. 2CYUCh. 11.1 - Prob. 3CYUCh. 11.1 - Prob. 4CYUCh. 11.1 - Prob. 5CYUCh. 11.1 - Prob. 6CYUCh. 11.1 - Prob. 7CYUCh. 11.1 - Prob. 8CYUCh. 11.1 - Prob. 9CYUCh. 11.1 - Prob. 10CYUCh. 11.1 - Prob. 11CYUCh. 11.1 - Prob. 12CYUCh. 11.1 - Prob. 13CYUCh. 11.1 - Prob. 14CYUCh. 11.1 - Prob. 15CYUCh. 11.1 - Prob. 16CYUCh. 11.1 - Prob. 17CYUCh. 11.1 - Prob. 18CYUCh. 11.1 - Prob. 19CYUCh. 11.1 - Prob. 20CYUCh. 11.1 - Prob. 21PPSCh. 11.1 - Prob. 22PPSCh. 11.1 - Prob. 23PPSCh. 11.1 - Prob. 24PPSCh. 11.1 - Prob. 25PPSCh. 11.1 - Prob. 26PPSCh. 11.1 - Prob. 27PPSCh. 11.1 - Prob. 28PPSCh. 11.1 - Prob. 29PPSCh. 11.1 - Prob. 30PPSCh. 11.1 - Prob. 31PPSCh. 11.1 - Prob. 32PPSCh. 11.1 - Prob. 33PPSCh. 11.1 - Prob. 34PPSCh. 11.1 - Prob. 35PPSCh. 11.1 - Prob. 36PPSCh. 11.1 - Prob. 37PPSCh. 11.1 - Prob. 38PPSCh. 11.1 - Prob. 39PPSCh. 11.1 - Prob. 40PPSCh. 11.1 - Prob. 41PPSCh. 11.1 - Prob. 42PPSCh. 11.1 - Prob. 43PPSCh. 11.1 - Prob. 44PPSCh. 11.1 - Prob. 45PPSCh. 11.1 - Prob. 46PPSCh. 11.1 - 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Prob. 97SCh. 11.2 - Prob. 98SCh. 11.2 - Prob. 99SCh. 11.2 - Prob. 100SCh. 11.3 - Prob. 1CYPCh. 11.3 - Prob. 2ACYPCh. 11.3 - Prob. 2BCYPCh. 11.3 - Prob. 3CYPCh. 11.3 - Prob. 4ACYPCh. 11.3 - Prob. 4BCYPCh. 11.3 - Prob. 5ACYPCh. 11.3 - Prob. 5BCYPCh. 11.3 - Prob. 6CYPCh. 11.3 - Prob. 1CYUCh. 11.3 - Prob. 2CYUCh. 11.3 - Prob. 3CYUCh. 11.3 - Prob. 4CYUCh. 11.3 - Prob. 5CYUCh. 11.3 - Prob. 6CYUCh. 11.3 - Prob. 7CYUCh. 11.3 - Prob. 8CYUCh. 11.3 - Prob. 9CYUCh. 11.3 - Prob. 10CYUCh. 11.3 - Prob. 11CYUCh. 11.3 - Prob. 12CYUCh. 11.3 - Prob. 13CYUCh. 11.3 - Prob. 14CYUCh. 11.3 - Prob. 15CYUCh. 11.3 - Prob. 16CYUCh. 11.3 - Prob. 17PPSCh. 11.3 - Prob. 18PPSCh. 11.3 - Prob. 19PPSCh. 11.3 - Prob. 20PPSCh. 11.3 - Prob. 21PPSCh. 11.3 - Prob. 22PPSCh. 11.3 - Prob. 23PPSCh. 11.3 - Prob. 24PPSCh. 11.3 - Prob. 25PPSCh. 11.3 - Prob. 26PPSCh. 11.3 - Prob. 27PPSCh. 11.3 - Prob. 28PPSCh. 11.3 - Prob. 29PPSCh. 11.3 - Prob. 30PPSCh. 11.3 - Prob. 31PPSCh. 11.3 - Prob. 32PPSCh. 11.3 - Prob. 33PPSCh. 11.3 - Prob. 34PPSCh. 11.3 - 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Prob. 82STPCh. 11.3 - Prob. 83STPCh. 11.3 - Prob. 84STPCh. 11.3 - Prob. 85STPCh. 11.3 - Prob. 86SCh. 11.3 - Prob. 87SCh. 11.3 - Prob. 88SCh. 11.3 - Prob. 89SCh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.4 - Prob. 1ACYPCh. 11.4 - Prob. 1BCYPCh. 11.4 - Prob. 2ACYPCh. 11.4 - Prob. 2BCYPCh. 11.4 - Prob. 3CYPCh. 11.4 - Prob. 4CYPCh. 11.4 - Prob. 1CYUCh. 11.4 - Prob. 2CYUCh. 11.4 - Prob. 3CYUCh. 11.4 - Prob. 4CYUCh. 11.4 - Prob. 5CYUCh. 11.4 - Prob. 6CYUCh. 11.4 - Prob. 7CYUCh. 11.4 - Prob. 8CYUCh. 11.4 - Prob. 9CYUCh. 11.4 - Prob. 10CYUCh. 11.4 - Prob. 11CYUCh. 11.4 - Prob. 12CYUCh. 11.4 - Prob. 13CYUCh. 11.4 - Prob. 14CYUCh. 11.4 - Prob. 15CYUCh. 11.4 - Prob. 16PPSCh. 11.4 - Prob. 17PPSCh. 11.4 - Prob. 18PPSCh. 11.4 - Prob. 19PPSCh. 11.4 - Prob. 20PPSCh. 11.4 - Prob. 21PPSCh. 11.4 - Prob. 22PPSCh. 11.4 - Prob. 23PPSCh. 11.4 - Prob. 24PPSCh. 11.4 - Prob. 25PPSCh. 11.4 - Prob. 26PPSCh. 11.4 - Prob. 27PPSCh. 11.4 - Prob. 28PPSCh. 11.4 - Prob. 29PPSCh. 11.4 - Prob. 30PPSCh. 11.4 - Prob. 31PPSCh. 11.4 - Prob. 32PPSCh. 11.4 - Prob. 33PPSCh. 11.4 - Prob. 34PPSCh. 11.4 - Prob. 35PPSCh. 11.4 - Prob. 36PPSCh. 11.4 - Prob. 37PPSCh. 11.4 - Prob. 38PPSCh. 11.4 - Prob. 39PPSCh. 11.4 - Prob. 40PPSCh. 11.4 - Prob. 41PPSCh. 11.4 - Prob. 42PPSCh. 11.4 - Prob. 43PPSCh. 11.4 - Prob. 44PPSCh. 11.4 - Prob. 45PPSCh. 11.4 - Prob. 46PPSCh. 11.4 - Prob. 47PPSCh. 11.4 - Prob. 48PPSCh. 11.4 - Prob. 49PPSCh. 11.4 - Prob. 50PPSCh. 11.4 - Prob. 51PPSCh. 11.4 - Prob. 52PPSCh. 11.4 - Prob. 53PPSCh. 11.4 - Prob. 54PPSCh. 11.4 - Prob. 55PPSCh. 11.4 - Prob. 56PPSCh. 11.4 - Prob. 57PPSCh. 11.4 - Prob. 58PPSCh. 11.4 - Prob. 59PPSCh. 11.4 - Prob. 60HPCh. 11.4 - Prob. 61HPCh. 11.4 - Prob. 62HPCh. 11.4 - Prob. 63HPCh. 11.4 - Prob. 64HPCh. 11.4 - Prob. 65HPCh. 11.4 - Prob. 66HPCh. 11.4 - Prob. 67HPCh. 11.4 - Prob. 68HPCh. 11.4 - Prob. 69HPCh. 11.4 - Prob. 70HPCh. 11.4 - Prob. 71HPCh. 11.4 - Prob. 72STPCh. 11.4 - Prob. 73STPCh. 11.4 - Prob. 74SCh. 11.4 - Prob. 75SCh. 11.4 - Prob. 76SCh. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.5 - Prob. 1CYPCh. 11.5 - Prob. 2ACYPCh. 11.5 - Prob. 2BCYPCh. 11.5 - Prob. 2CCYPCh. 11.5 - Prob. 3CYPCh. 11.5 - Prob. 4CYPCh. 11.5 - Prob. 1CYUCh. 11.5 - Prob. 2CYUCh. 11.5 - Prob. 3CYUCh. 11.5 - Prob. 4CYUCh. 11.5 - Prob. 5CYUCh. 11.5 - Prob. 6CYUCh. 11.5 - Prob. 7CYUCh. 11.5 - Prob. 8CYUCh. 11.5 - Prob. 9CYUCh. 11.5 - Prob. 10CYUCh. 11.5 - Prob. 11CYUCh. 11.5 - Prob. 12PPSCh. 11.5 - Prob. 13PPSCh. 11.5 - Prob. 14PPSCh. 11.5 - Prob. 15PPSCh. 11.5 - Prob. 16PPSCh. 11.5 - Prob. 17PPSCh. 11.5 - Prob. 18PPSCh. 11.5 - Prob. 19PPSCh. 11.5 - Prob. 20PPSCh. 11.5 - Prob. 21PPSCh. 11.5 - Prob. 22PPSCh. 11.5 - Prob. 23PPSCh. 11.5 - Prob. 24PPSCh. 11.5 - Prob. 25PPSCh. 11.5 - Prob. 26PPSCh. 11.5 - Prob. 27PPSCh. 11.5 - Prob. 28PPSCh. 11.5 - Prob. 29PPSCh. 11.5 - Prob. 30PPSCh. 11.5 - Prob. 31PPSCh. 11.5 - Prob. 32PPSCh. 11.5 - Prob. 33PPSCh. 11.5 - Prob. 34PPSCh. 11.5 - Prob. 35PPSCh. 11.5 - Prob. 36PPSCh. 11.5 - 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Publisher:Cengage Learning
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Publisher:PEARSON
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Sequences and Series (Arithmetic & Geometric) Quick Review; Author: Mario's Math Tutoring;https://www.youtube.com/watch?v=Tj89FA-d0f8;License: Standard YouTube License, CC-BY