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 67HP
To determine

To explain why an arithmetic series is always divergent.

Expert Solution & Answer
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Answer to Problem 67HP

An arithmetic series is always divergent

Explanation of Solution

Given:

An infinite arithmetic series.

Concept Used:

Sum of first n terms of an arithmetic series whose first term is a and common difference d is:

  Sn=n(2a+(n1)d)2

Calculation:

To explain why an arithmetic series is always divergent.

First consider an infinite arithmetic series

  a+(a+d)+(a+2d)+(a+3d)......=n=0(a+nd) .

Then sum of its n term is given by the formula:

  Sn=n(2a+(n1)d)2=(ad2)n+d2n2

Note that both the terms of above sum tends to infinity as n tends to infinity, i.e.

  (ad2)n; and d2n2When n

Thus, the above sum diverges a n tends to infinity, since

  Sn=(ad2)n+d2n2=+ when n=

Thus, an arithmetic series is always divergent.

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 - 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 - Prob. 37PPSCh. 11.5 - Prob. 38PPSCh. 11.5 - Prob. 39PPSCh. 11.5 - Prob. 40PPSCh. 11.5 - Prob. 41PPSCh. 11.5 - Prob. 42PPSCh. 11.5 - Prob. 43PPSCh. 11.5 - Prob. 44PPSCh. 11.5 - Prob. 45PPSCh. 11.5 - Prob. 46PPSCh. 11.5 - Prob. 47PPSCh. 11.5 - Prob. 48PPSCh. 11.5 - Prob. 49HPCh. 11.5 - Prob. 50HPCh. 11.5 - Prob. 51HPCh. 11.5 - Prob. 52HPCh. 11.5 - Prob. 53HPCh. 11.5 - Prob. 54HPCh. 11.5 - Prob. 55HPCh. 11.5 - Prob. 56HPCh. 11.5 - Prob. 57HPCh. 11.5 - Prob. 58STPCh. 11.5 - Prob. 59STPCh. 11.5 - Prob. 60STPCh. 11.5 - Prob. 61STPCh. 11.5 - Prob. 62STPCh. 11.5 - Prob. 63STPCh. 11.5 - Prob. 64SCh. 11.5 - Prob. 65SCh. 11.5 - Prob. 66SCh. 11.5 - Prob. 67SCh. 11.5 - Prob. 68SCh. 11.5 - Prob. 69SCh. 11.6 - Prob. 1CYPCh. 11.6 - Prob. 2CYPCh. 11.6 - Prob. 3CYPCh. 11.6 - Prob. 4CYPCh. 11.6 - Prob. 1CYUCh. 11.6 - Prob. 2CYUCh. 11.6 - Prob. 3CYUCh. 11.6 - Prob. 4CYUCh. 11.6 - Prob. 5CYUCh. 11.6 - Prob. 6CYUCh. 11.6 - Prob. 7CYUCh. 11.6 - Prob. 8CYUCh. 11.6 - Prob. 9CYUCh. 11.6 - Prob. 10CYUCh. 11.6 - 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Prob. 3CYUCh. 11.7 - Prob. 4CYUCh. 11.7 - Prob. 5CYUCh. 11.7 - Prob. 6CYUCh. 11.7 - Prob. 7CYUCh. 11.7 - Prob. 8PPSCh. 11.7 - Prob. 9PPSCh. 11.7 - Prob. 10PPSCh. 11.7 - Prob. 11PPSCh. 11.7 - Prob. 12PPSCh. 11.7 - Prob. 13PPSCh. 11.7 - Prob. 14PPSCh. 11.7 - Prob. 15PPSCh. 11.7 - Prob. 16PPSCh. 11.7 - Prob. 17PPSCh. 11.7 - Prob. 18PPSCh. 11.7 - Prob. 19PPSCh. 11.7 - Prob. 20PPSCh. 11.7 - Prob. 21PPSCh. 11.7 - Prob. 22PPSCh. 11.7 - Prob. 23PPSCh. 11.7 - Prob. 24PPSCh. 11.7 - Prob. 25PPSCh. 11.7 - Prob. 26PPSCh. 11.7 - Prob. 27PPSCh. 11.7 - Prob. 28PPSCh. 11.7 - Prob. 29PPSCh. 11.7 - Prob. 30PPSCh. 11.7 - Prob. 31PPSCh. 11.7 - Prob. 32PPSCh. 11.7 - Prob. 33HPCh. 11.7 - Prob. 34HPCh. 11.7 - Prob. 35HPCh. 11.7 - Prob. 36HPCh. 11.7 - Prob. 37HPCh. 11.7 - Prob. 38HPCh. 11.7 - Prob. 39HPCh. 11.7 - Prob. 40HPCh. 11.7 - Prob. 41HPCh. 11.7 - Prob. 42HPCh. 11.7 - Prob. 43HPCh. 11.7 - Prob. 44HPCh. 11.7 - Prob. 45STPCh. 11.7 - Prob. 46STPCh. 11.7 - Prob. 47STPCh. 11.7 - Prob. 48STPCh. 11.7 - Prob. 49STPCh. 11.7 - 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Publisher:Wellesley-Cambridge Press
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College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education
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