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 47PPS
To determine

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

  158+52+103+......

Expert Solution & Answer
Check Mark

Answer to Problem 47PPS

The sum does not exist.

Explanation of Solution

Given:

  158+52+103+......

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>1 does not exist.

Calculation:

In order to find the sum of infinite series

  158+52+103+......

First find its first term and common ratio.

Note from the given infinite series that first term is 158 , and the common ratio ( r ) can be find by dividing second term by first term, as

  r=a2a1

Since, here

  a2=52,a1=158

Thus,

  r=52158=52×815=43=1.33

Since, the common ratio of the series is greater than 1.

Thus, the sum of the infinite series does not exist.

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 - Prob. 47PPSCh. 11.1 - Prob. 48PPSCh. 11.1 - Prob. 49PPSCh. 11.1 - Prob. 50PPSCh. 11.1 - Prob. 51PPSCh. 11.1 - Prob. 52PPSCh. 11.1 - Prob. 53PPSCh. 11.1 - Prob. 54HPCh. 11.1 - Prob. 55HPCh. 11.1 - Prob. 56HPCh. 11.1 - Prob. 57HPCh. 11.1 - Prob. 58HPCh. 11.1 - Prob. 59HPCh. 11.1 - Prob. 60HPCh. 11.1 - Prob. 61HPCh. 11.1 - Prob. 62HPCh. 11.1 - Prob. 63HPCh. 11.1 - Prob. 64HPCh. 11.1 - Prob. 65STPCh. 11.1 - Prob. 66STPCh. 11.1 - Prob. 67STPCh. 11.1 - Prob. 68STPCh. 11.1 - Prob. 69STPCh. 11.1 - Prob. 70STPCh. 11.1 - Prob. 71STPCh. 11.1 - Prob. 72STPCh. 11.1 - Prob. 73STPCh. 11.1 - Prob. 74STPCh. 11.1 - Prob. 75SCh. 11.1 - Prob. 76SCh. 11.1 - Prob. 77SCh. 11.1 - Prob. 78SCh. 11.1 - Prob. 79SCh. 11.1 - Prob. 80SCh. 11.2 - Prob. 1ACYPCh. 11.2 - Prob. 1BCYPCh. 11.2 - Prob. 2ACYPCh. 11.2 - Prob. 2BCYPCh. 11.2 - Prob. 3CYPCh. 11.2 - Prob. 4ACYPCh. 11.2 - Prob. 4BCYPCh. 11.2 - Prob. 5ACYPCh. 11.2 - Prob. 5BCYPCh. 11.2 - Prob. 6CYPCh. 11.2 - Prob. 1CYUCh. 11.2 - Prob. 2CYUCh. 11.2 - Prob. 3CYUCh. 11.2 - Prob. 4CYUCh. 11.2 - Prob. 5CYUCh. 11.2 - Prob. 6CYUCh. 11.2 - Prob. 7CYUCh. 11.2 - Prob. 8CYUCh. 11.2 - Prob. 9CYUCh. 11.2 - Prob. 10CYUCh. 11.2 - Prob. 11CYUCh. 11.2 - Prob. 12CYUCh. 11.2 - Prob. 13CYUCh. 11.2 - Prob. 14PPSCh. 11.2 - Prob. 15PPSCh. 11.2 - Prob. 16PPSCh. 11.2 - Prob. 17PPSCh. 11.2 - Prob. 18PPSCh. 11.2 - Prob. 19PPSCh. 11.2 - Prob. 20PPSCh. 11.2 - Prob. 21PPSCh. 11.2 - Prob. 22PPSCh. 11.2 - Prob. 23PPSCh. 11.2 - Prob. 24PPSCh. 11.2 - Prob. 25PPSCh. 11.2 - Prob. 26PPSCh. 11.2 - Prob. 27PPSCh. 11.2 - Prob. 28PPSCh. 11.2 - Prob. 29PPSCh. 11.2 - Prob. 30PPSCh. 11.2 - Prob. 31PPSCh. 11.2 - Prob. 32PPSCh. 11.2 - Prob. 33PPSCh. 11.2 - Prob. 34PPSCh. 11.2 - Prob. 35PPSCh. 11.2 - Prob. 36PPSCh. 11.2 - Prob. 37PPSCh. 11.2 - Prob. 38PPSCh. 11.2 - Prob. 39PPSCh. 11.2 - Prob. 40PPSCh. 11.2 - Prob. 41PPSCh. 11.2 - Prob. 42PPSCh. 11.2 - Prob. 43PPSCh. 11.2 - Prob. 44PPSCh. 11.2 - Prob. 45PPSCh. 11.2 - Prob. 46PPSCh. 11.2 - Prob. 47PPSCh. 11.2 - Prob. 48PPSCh. 11.2 - Prob. 49PPSCh. 11.2 - 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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 - Prob. 35PPSCh. 11.3 - Prob. 36PPSCh. 11.3 - Prob. 37PPSCh. 11.3 - Prob. 38PPSCh. 11.3 - Prob. 39PPSCh. 11.3 - Prob. 40PPSCh. 11.3 - Prob. 41PPSCh. 11.3 - Prob. 42PPSCh. 11.3 - Prob. 43PPSCh. 11.3 - Prob. 44PPSCh. 11.3 - Prob. 45PPSCh. 11.3 - Prob. 46PPSCh. 11.3 - Prob. 47PPSCh. 11.3 - Prob. 48PPSCh. 11.3 - Prob. 49PPSCh. 11.3 - Prob. 50PPSCh. 11.3 - Prob. 51PPSCh. 11.3 - Prob. 52PPSCh. 11.3 - Prob. 53PPSCh. 11.3 - Prob. 54PPSCh. 11.3 - Prob. 55PPSCh. 11.3 - Prob. 56PPSCh. 11.3 - Prob. 57PPSCh. 11.3 - Prob. 58PPSCh. 11.3 - Prob. 59PPSCh. 11.3 - Prob. 60PPSCh. 11.3 - Prob. 61PPSCh. 11.3 - Prob. 62PPSCh. 11.3 - Prob. 63PPSCh. 11.3 - Prob. 64HPCh. 11.3 - Prob. 65HPCh. 11.3 - Prob. 66HPCh. 11.3 - Prob. 67HPCh. 11.3 - Prob. 68HPCh. 11.3 - Prob. 69HPCh. 11.3 - Prob. 70HPCh. 11.3 - Prob. 71HPCh. 11.3 - Prob. 72HPCh. 11.3 - Prob. 73HPCh. 11.3 - Prob. 74HPCh. 11.3 - Prob. 75HPCh. 11.3 - Prob. 76HPCh. 11.3 - Prob. 77STPCh. 11.3 - Prob. 78STPCh. 11.3 - Prob. 79STPCh. 11.3 - Prob. 80STPCh. 11.3 - Prob. 81STPCh. 11.3 - 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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Prob. 11CYUCh. 11.6 - Prob. 12CYUCh. 11.6 - Prob. 13CYUCh. 11.6 - Prob. 14CYUCh. 11.6 - Prob. 15PPSCh. 11.6 - Prob. 16PPSCh. 11.6 - Prob. 17PPSCh. 11.6 - Prob. 18PPSCh. 11.6 - Prob. 19PPSCh. 11.6 - Prob. 20PPSCh. 11.6 - Prob. 21PPSCh. 11.6 - Prob. 22PPSCh. 11.6 - Prob. 23PPSCh. 11.6 - Prob. 24PPSCh. 11.6 - Prob. 25PPSCh. 11.6 - Prob. 26PPSCh. 11.6 - Prob. 27PPSCh. 11.6 - Prob. 28PPSCh. 11.6 - Prob. 29PPSCh. 11.6 - Prob. 30PPSCh. 11.6 - Prob. 31PPSCh. 11.6 - Prob. 32PPSCh. 11.6 - Prob. 33PPSCh. 11.6 - Prob. 34HPCh. 11.6 - Prob. 35HPCh. 11.6 - Prob. 36HPCh. 11.6 - Prob. 37HPCh. 11.6 - Prob. 38HPCh. 11.6 - Prob. 39HPCh. 11.6 - Prob. 40HPCh. 11.6 - Prob. 41HPCh. 11.6 - Prob. 42HPCh. 11.6 - Prob. 43STPCh. 11.6 - Prob. 44STPCh. 11.6 - Prob. 45STPCh. 11.6 - Prob. 46STPCh. 11.6 - Prob. 47STPCh. 11.6 - Prob. 48STPCh. 11.6 - Prob. 49STPCh. 11.6 - Prob. 50SCh. 11.6 - Prob. 51SCh. 11.6 - Prob. 52SCh. 11.7 - Prob. 1CYPCh. 11.7 - Prob. 2CYPCh. 11.7 - Prob. 3CYPCh. 11.7 - Prob. 1CYUCh. 11.7 - Prob. 2CYUCh. 11.7 - 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Prob. 50STPCh. 11.7 - Prob. 51SCh. 11.7 - Prob. 52SCh. 11.7 - Prob. 53SCh. 11.7 - Prob. 54SCh. 11.7 - Prob. 55SCh. 11.7 - Prob. 56SCh. 11.7 - Prob. 57SCh. 11.7 - Prob. 58SCh. 11.7 - Prob. 59SCh. 11.7 - Prob. 60SCh. 11.7 - Prob. 61SCh. 11.7 - Prob. 62SCh. 11 - Prob. 1QCCh. 11 - Prob. 2QCCh. 11 - Prob. 3QCCh. 11 - Prob. 4QCCh. 11 - Prob. 5QCCh. 11 - Prob. 6QCCh. 11 - Prob. 7QCCh. 11 - Prob. 8QCCh. 11 - Prob. 9QCCh. 11 - Prob. 10QCCh. 11 - Prob. 11QCCh. 11 - Prob. 12QCCh. 11 - Prob. 13QCCh. 11 - Prob. 14QCCh. 11 - Prob. 1MCQCh. 11 - Prob. 2MCQCh. 11 - Prob. 3MCQCh. 11 - Prob. 4MCQCh. 11 - Prob. 5MCQCh. 11 - Prob. 6MCQCh. 11 - Prob. 7MCQCh. 11 - Prob. 8MCQCh. 11 - Prob. 9MCQCh. 11 - Prob. 10MCQCh. 11 - Prob. 11MCQCh. 11 - Prob. 12MCQCh. 11 - Prob. 13MCQCh. 11 - Prob. 14MCQCh. 11 - Prob. 15MCQCh. 11 - Prob. 16MCQCh. 11 - Prob. 17MCQCh. 11 - Prob. 18MCQCh. 11 - Prob. 19MCQCh. 11 - Prob. 20MCQCh. 11 - Prob. 1SGRCh. 11 - Prob. 2SGRCh. 11 - Prob. 3SGRCh. 11 - Prob. 4SGRCh. 11 - Prob. 5SGRCh. 11 - Prob. 6SGRCh. 11 - Prob. 7SGRCh. 11 - Prob. 8SGRCh. 11 - Prob. 9SGRCh. 11 - Prob. 10SGRCh. 11 - Prob. 11SGRCh. 11 - Prob. 12SGRCh. 11 - Prob. 13SGRCh. 11 - Prob. 14SGRCh. 11 - Prob. 15SGRCh. 11 - Prob. 16SGRCh. 11 - Prob. 17SGRCh. 11 - Prob. 18SGRCh. 11 - Prob. 19SGRCh. 11 - Prob. 20SGRCh. 11 - Prob. 21SGRCh. 11 - Prob. 22SGRCh. 11 - Prob. 23SGRCh. 11 - Prob. 24SGRCh. 11 - Prob. 25SGRCh. 11 - Prob. 26SGRCh. 11 - Prob. 27SGRCh. 11 - Prob. 28SGRCh. 11 - Prob. 29SGRCh. 11 - Prob. 30SGRCh. 11 - Prob. 31SGRCh. 11 - Prob. 32SGRCh. 11 - Prob. 33SGRCh. 11 - Prob. 34SGRCh. 11 - Prob. 35SGRCh. 11 - Prob. 36SGRCh. 11 - Prob. 37SGRCh. 11 - Prob. 38SGRCh. 11 - Prob. 39SGRCh. 11 - Prob. 40SGRCh. 11 - Prob. 41SGRCh. 11 - Prob. 42SGRCh. 11 - Prob. 43SGRCh. 11 - Prob. 44SGRCh. 11 - Prob. 45SGRCh. 11 - Prob. 46SGRCh. 11 - Prob. 47SGRCh. 11 - Prob. 48SGRCh. 11 - Prob. 49SGRCh. 11 - Prob. 50SGRCh. 11 - Prob. 51SGRCh. 11 - Prob. 52SGRCh. 11 - Prob. 53SGRCh. 11 - Prob. 54SGRCh. 11 - Prob. 55SGRCh. 11 - Prob. 56SGRCh. 11 - 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Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
Text book image
College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education
Sequences and Series Introduction; Author: Mario's Math Tutoring;https://www.youtube.com/watch?v=m5Yn4BdpOV0;License: Standard YouTube License, CC-BY
Introduction to sequences; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=VG9ft4_dK24;License: Standard YouTube License, CC-BY