Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
1st Edition
ISBN: 9780078682278
Author: McGraw-Hill, Berchie Holliday
Publisher: Glencoe/McGraw-Hill
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Chapter 12.4, Problem 6CFU
To determine

To determine whether given series is convergent or divergent using ratio test.

Expert Solution & Answer
Check Mark

Answer to Problem 6CFU

The test provides no information.

Explanation of Solution

Given information:

  34+78+1112+1516+...

Concept used:

Ratio Test: Let an be a sequence of non-negative terms. n=1an be the corresponding series.

Let, L=limnan+1an exists.Then, ratio test says that,

  1. If L<1then series converges.
  2. If L>1 then series diverges.
  3. If L=1 then test fails.

Calculation:

  34+78+1112+1516+...

Find an and an+1

  an=4n14n , an+1=4(n+1)14(n+1)=4n+34n+4

Then,

  L=limnan+1an=limn4n+34n+44n14n=limn(4n+34n+4×4n4n1)=limn(1+34n1+44n)limn(1114n)=1

Since L=1 , the test provides no information.

Chapter 12 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 12.1 - Prob. 11CFUCh. 12.1 - Prob. 12CFUCh. 12.1 - Prob. 13CFUCh. 12.1 - Prob. 14CFUCh. 12.1 - Prob. 15CFUCh. 12.1 - Prob. 16CFUCh. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.1 - Prob. 28ECh. 12.1 - Prob. 29ECh. 12.1 - Prob. 30ECh. 12.1 - Prob. 31ECh. 12.1 - Prob. 32ECh. 12.1 - Prob. 33ECh. 12.1 - Prob. 34ECh. 12.1 - Prob. 35ECh. 12.1 - Prob. 36ECh. 12.1 - Prob. 37ECh. 12.1 - Prob. 38ECh. 12.1 - Prob. 39ECh. 12.1 - Prob. 40ECh. 12.1 - Prob. 41ECh. 12.1 - Prob. 42ECh. 12.1 - Prob. 43ECh. 12.1 - Prob. 44ECh. 12.1 - Prob. 45ECh. 12.1 - Prob. 46ECh. 12.1 - Prob. 47ECh. 12.1 - Prob. 48ECh. 12.1 - Prob. 49ECh. 12.1 - Prob. 50ECh. 12.1 - Prob. 51ECh. 12.1 - Prob. 52ECh. 12.1 - Prob. 53ECh. 12.1 - Prob. 54ECh. 12.1 - Prob. 55ECh. 12.1 - Prob. 56ECh. 12.1 - Prob. 57ECh. 12.1 - Prob. 58ECh. 12.1 - Prob. 59ECh. 12.1 - Prob. 60ECh. 12.1 - Prob. 61ECh. 12.1 - Prob. 62ECh. 12.1 - Prob. 63ECh. 12.1 - Prob. 64ECh. 12.1 - Prob. 65ECh. 12.1 - Prob. 66ECh. 12.1 - Prob. 67ECh. 12.1 - Prob. 68ECh. 12.1 - Prob. 69ECh. 12.2 - Prob. 1CFUCh. 12.2 - Prob. 2CFUCh. 12.2 - Prob. 3CFUCh. 12.2 - Prob. 4CFUCh. 12.2 - Prob. 5CFUCh. 12.2 - Prob. 6CFUCh. 12.2 - Prob. 7CFUCh. 12.2 - Prob. 8CFUCh. 12.2 - Prob. 9CFUCh. 12.2 - Prob. 10CFUCh. 12.2 - Prob. 11CFUCh. 12.2 - Prob. 12CFUCh. 12.2 - Prob. 13CFUCh. 12.2 - Prob. 14CFUCh. 12.2 - Prob. 15CFUCh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.2 - Prob. 23ECh. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Prob. 27ECh. 12.2 - Prob. 28ECh. 12.2 - Prob. 29ECh. 12.2 - Prob. 30ECh. 12.2 - Prob. 31ECh. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Prob. 35ECh. 12.2 - Prob. 36ECh. 12.2 - Prob. 37ECh. 12.2 - Prob. 38ECh. 12.2 - Prob. 39ECh. 12.2 - Prob. 40ECh. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Prob. 44ECh. 12.2 - Prob. 45ECh. 12.2 - Prob. 46ECh. 12.2 - Prob. 47ECh. 12.2 - Prob. 48ECh. 12.2 - Prob. 49ECh. 12.2 - Prob. 50ECh. 12.2 - Prob. 51ECh. 12.2 - Prob. 52ECh. 12.2 - Prob. 53ECh. 12.2 - Prob. 54ECh. 12.2 - Prob. 55ECh. 12.2 - Prob. 56ECh. 12.2 - Prob. 57ECh. 12.3 - Prob. 1CFUCh. 12.3 - Prob. 2CFUCh. 12.3 - Prob. 3CFUCh. 12.3 - Prob. 4CFUCh. 12.3 - Prob. 5CFUCh. 12.3 - Prob. 6CFUCh. 12.3 - Prob. 7CFUCh. 12.3 - Prob. 8CFUCh. 12.3 - Prob. 9CFUCh. 12.3 - Prob. 10CFUCh. 12.3 - Prob. 11CFUCh. 12.3 - Prob. 12CFUCh. 12.3 - Prob. 13CFUCh. 12.3 - Prob. 14ECh. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Prob. 20ECh. 12.3 - Prob. 21ECh. 12.3 - Prob. 22ECh. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.3 - Prob. 27ECh. 12.3 - Prob. 28ECh. 12.3 - Prob. 29ECh. 12.3 - Prob. 30ECh. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Prob. 33ECh. 12.3 - Prob. 34ECh. 12.3 - Prob. 35ECh. 12.3 - Prob. 36ECh. 12.3 - Prob. 37ECh. 12.3 - Prob. 38ECh. 12.3 - Prob. 39ECh. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Prob. 42ECh. 12.3 - Prob. 43ECh. 12.3 - Prob. 44ECh. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 - Prob. 47ECh. 12.3 - Prob. 48ECh. 12.3 - Prob. 49ECh. 12.3 - Prob. 50ECh. 12.3 - Prob. 51ECh. 12.3 - Prob. 52ECh. 12.3 - Prob. 53ECh. 12.3 - Prob. 54ECh. 12.3 - Prob. 55ECh. 12.3B - Prob. 1GCECh. 12.3B - Prob. 2GCECh. 12.3B - Prob. 3GCECh. 12.3B - Prob. 4GCECh. 12.3B - Prob. 5GCECh. 12.3B - Prob. 6GCECh. 12.3B - Prob. 7GCECh. 12.3B - Prob. 8GCECh. 12.3B - Prob. 9GCECh. 12.3B - Prob. 10GCECh. 12.3B - Prob. 11GCECh. 12.4 - Prob. 1CFUCh. 12.4 - Prob. 2CFUCh. 12.4 - Prob. 3CFUCh. 12.4 - Prob. 4CFUCh. 12.4 - Prob. 5CFUCh. 12.4 - Prob. 6CFUCh. 12.4 - Prob. 7CFUCh. 12.4 - Prob. 8CFUCh. 12.4 - Prob. 9CFUCh. 12.4 - Prob. 10CFUCh. 12.4 - Prob. 11CFUCh. 12.4 - Prob. 12CFUCh. 12.4 - Prob. 13ECh. 12.4 - Prob. 14ECh. 12.4 - Prob. 15ECh. 12.4 - Prob. 16ECh. 12.4 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Prob. 19ECh. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - Prob. 25ECh. 12.4 - Prob. 26ECh. 12.4 - Prob. 27ECh. 12.4 - Prob. 28ECh. 12.4 - Prob. 29ECh. 12.4 - Prob. 30ECh. 12.4 - Prob. 31ECh. 12.4 - Prob. 32ECh. 12.4 - Prob. 33ECh. 12.4 - Prob. 34ECh. 12.4 - Prob. 35ECh. 12.4 - Prob. 36ECh. 12.4 - Prob. 37ECh. 12.4 - Prob. 38ECh. 12.4 - Prob. 39ECh. 12.4 - Prob. 40ECh. 12.4 - Prob. 41ECh. 12.4 - Prob. 42ECh. 12.4 - Prob. 1MCQCh. 12.4 - Prob. 2MCQCh. 12.4 - Prob. 3MCQCh. 12.4 - Prob. 4MCQCh. 12.4 - Prob. 5MCQCh. 12.4 - Prob. 6MCQCh. 12.4 - Prob. 7MCQCh. 12.4 - Prob. 8MCQCh. 12.4 - Prob. 9MCQCh. 12.4 - Prob. 10MCQCh. 12.5 - Prob. 1CFUCh. 12.5 - Prob. 2CFUCh. 12.5 - Prob. 3CFUCh. 12.5 - Prob. 4CFUCh. 12.5 - Prob. 5CFUCh. 12.5 - Prob. 6CFUCh. 12.5 - Prob. 7CFUCh. 12.5 - Prob. 8CFUCh. 12.5 - Prob. 9CFUCh. 12.5 - Prob. 10CFUCh. 12.5 - Prob. 11CFUCh. 12.5 - Prob. 12CFUCh. 12.5 - Prob. 13CFUCh. 12.5 - Prob. 14ECh. 12.5 - Prob. 15ECh. 12.5 - Prob. 16ECh. 12.5 - Prob. 17ECh. 12.5 - Prob. 18ECh. 12.5 - Prob. 19ECh. 12.5 - Prob. 20ECh. 12.5 - Prob. 21ECh. 12.5 - Prob. 22ECh. 12.5 - Prob. 23ECh. 12.5 - Prob. 24ECh. 12.5 - Prob. 25ECh. 12.5 - Prob. 26ECh. 12.5 - Prob. 27ECh. 12.5 - Prob. 28ECh. 12.5 - Prob. 29ECh. 12.5 - Prob. 30ECh. 12.5 - Prob. 31ECh. 12.5 - Prob. 32ECh. 12.5 - Prob. 33ECh. 12.5 - Prob. 34ECh. 12.5 - Prob. 35ECh. 12.5 - Prob. 36ECh. 12.5 - Prob. 37ECh. 12.5 - Prob. 38ECh. 12.5 - Prob. 39ECh. 12.5 - Prob. 40ECh. 12.5 - Prob. 41ECh. 12.5 - Prob. 42ECh. 12.5 - Prob. 43ECh. 12.5 - Prob. 44ECh. 12.5 - Prob. 45ECh. 12.5 - Prob. 46ECh. 12.5 - Prob. 47ECh. 12.5 - Prob. 48ECh. 12.5 - Prob. 49ECh. 12.5 - Prob. 50ECh. 12.5 - Prob. 51ECh. 12.5 - Prob. 52ECh. 12.5 - Prob. 53ECh. 12.5 - Prob. 54ECh. 12.5 - Prob. 55ECh. 12.5 - Prob. 56ECh. 12.5 - Prob. 57ECh. 12.5 - Prob. 58ECh. 12.5 - Prob. 59ECh. 12.6 - Prob. 1CFUCh. 12.6 - Prob. 2CFUCh. 12.6 - Prob. 3CFUCh. 12.6 - Prob. 4CFUCh. 12.6 - Prob. 5CFUCh. 12.6 - Prob. 6CFUCh. 12.6 - Prob. 7CFUCh. 12.6 - Prob. 8CFUCh. 12.6 - Prob. 9CFUCh. 12.6 - Prob. 10CFUCh. 12.6 - Prob. 11CFUCh. 12.6 - Prob. 12CFUCh. 12.6 - Prob. 13ECh. 12.6 - Prob. 14ECh. 12.6 - Prob. 15ECh. 12.6 - Prob. 16ECh. 12.6 - Prob. 17ECh. 12.6 - Prob. 18ECh. 12.6 - Prob. 19ECh. 12.6 - Prob. 20ECh. 12.6 - Prob. 21ECh. 12.6 - Prob. 22ECh. 12.6 - Prob. 23ECh. 12.6 - Prob. 24ECh. 12.6 - Prob. 25ECh. 12.6 - Prob. 26ECh. 12.6 - Prob. 27ECh. 12.6 - Prob. 28ECh. 12.6 - Prob. 29ECh. 12.6 - Prob. 30ECh. 12.6 - Prob. 31ECh. 12.6 - Prob. 32ECh. 12.6 - Prob. 33ECh. 12.6 - Prob. 34ECh. 12.6 - Prob. 35ECh. 12.6 - Prob. 36ECh. 12.6 - Prob. 37ECh. 12.6 - Prob. 38ECh. 12.6 - Prob. 39ECh. 12.6 - Prob. 40ECh. 12.6 - Prob. 41ECh. 12.6 - Prob. 42ECh. 12.6 - Prob. 43ECh. 12.6 - Prob. 44ECh. 12.7 - Prob. 1GCECh. 12.7 - Prob. 2GCECh. 12.7 - Prob. 3GCECh. 12.7 - Prob. 4GCECh. 12.7 - Prob. 5GCECh. 12.7 - Prob. 6GCECh. 12.7 - Prob. 1CFUCh. 12.7 - Prob. 2CFUCh. 12.7 - Prob. 3CFUCh. 12.7 - Prob. 4CFUCh. 12.7 - Prob. 5CFUCh. 12.7 - Prob. 6CFUCh. 12.7 - Prob. 7CFUCh. 12.7 - Prob. 8CFUCh. 12.7 - Prob. 9CFUCh. 12.7 - Prob. 10CFUCh. 12.7 - Prob. 11CFUCh. 12.7 - Prob. 12CFUCh. 12.7 - Prob. 13ECh. 12.7 - Prob. 14ECh. 12.7 - Prob. 15ECh. 12.7 - Prob. 16ECh. 12.7 - Prob. 17ECh. 12.7 - Prob. 18ECh. 12.7 - Prob. 19ECh. 12.7 - Prob. 20ECh. 12.7 - Prob. 21ECh. 12.7 - Prob. 22ECh. 12.7 - Prob. 23ECh. 12.7 - Prob. 24ECh. 12.7 - Prob. 25ECh. 12.7 - Prob. 26ECh. 12.7 - Prob. 27ECh. 12.7 - Prob. 28ECh. 12.7 - Prob. 29ECh. 12.7 - Prob. 30ECh. 12.7 - Prob. 31ECh. 12.7 - Prob. 32ECh. 12.7 - Prob. 33ECh. 12.7 - Prob. 34ECh. 12.7 - Prob. 35ECh. 12.7 - Prob. 36ECh. 12.7 - Prob. 37ECh. 12.7 - Prob. 39ECh. 12.7 - Prob. 40ECh. 12.7 - Prob. 41ECh. 12.7 - Prob. 42ECh. 12.7 - Prob. 43ECh. 12.7 - Prob. 44ECh. 12.7 - Prob. 45ECh. 12.7 - Prob. 46ECh. 12.7 - Prob. 47ECh. 12.7 - Prob. 48ECh. 12.7 - Prob. 49ECh. 12.7 - Prob. 50ECh. 12.7 - Prob. 51ECh. 12.7 - Prob. 52ECh. 12.8 - Prob. 1CFUCh. 12.8 - Prob. 2CFUCh. 12.8 - Prob. 3CFUCh. 12.8 - Prob. 4CFUCh. 12.8 - Prob. 5CFUCh. 12.8 - Prob. 6CFUCh. 12.8 - Prob. 7CFUCh. 12.8 - Prob. 8CFUCh. 12.8 - Prob. 9CFUCh. 12.8 - Prob. 10CFUCh. 12.8 - Prob. 11ECh. 12.8 - Prob. 12ECh. 12.8 - Prob. 13ECh. 12.8 - Prob. 14ECh. 12.8 - Prob. 15ECh. 12.8 - Prob. 16ECh. 12.8 - Prob. 17ECh. 12.8 - Prob. 18ECh. 12.8 - Prob. 19ECh. 12.8 - Prob. 20ECh. 12.8 - Prob. 21ECh. 12.8 - Prob. 22ECh. 12.8 - Prob. 23ECh. 12.8 - Prob. 24ECh. 12.8 - Prob. 25ECh. 12.8 - Prob. 26ECh. 12.8 - Prob. 27ECh. 12.8 - Prob. 28ECh. 12.8 - Prob. 29ECh. 12.8 - Prob. 30ECh. 12.8 - Prob. 31ECh. 12.8 - Prob. 32ECh. 12.8 - Prob. 33ECh. 12.8 - Prob. 35ECh. 12.8 - Prob. 36ECh. 12.8 - Prob. 37ECh. 12.8 - Prob. 38ECh. 12.8 - Prob. 39ECh. 12.8 - Prob. 40ECh. 12.8 - Prob. 41ECh. 12.8 - Prob. 42ECh. 12.8 - Prob. 43ECh. 12.8 - Prob. 44ECh. 12.9 - Prob. 1CFUCh. 12.9 - Prob. 2CFUCh. 12.9 - Prob. 3CFUCh. 12.9 - Prob. 4CFUCh. 12.9 - Prob. 5CFUCh. 12.9 - Prob. 6CFUCh. 12.9 - Prob. 7CFUCh. 12.9 - Prob. 8CFUCh. 12.9 - Prob. 9CFUCh. 12.9 - Prob. 10CFUCh. 12.9 - Prob. 11ECh. 12.9 - Prob. 12ECh. 12.9 - Prob. 13ECh. 12.9 - Prob. 14ECh. 12.9 - Prob. 15ECh. 12.9 - Prob. 16ECh. 12.9 - Prob. 17ECh. 12.9 - Prob. 18ECh. 12.9 - Prob. 19ECh. 12.9 - Prob. 20ECh. 12.9 - Prob. 21ECh. 12.9 - Prob. 22ECh. 12.9 - Prob. 23ECh. 12.9 - Prob. 24ECh. 12.9 - Prob. 25ECh. 12.9 - Prob. 26ECh. 12.9 - Prob. 27ECh. 12.9 - Prob. 28ECh. 12.9 - Prob. 29ECh. 12.9 - Prob. 30ECh. 12.9 - Prob. 31ECh. 12.9 - Prob. 32ECh. 12.9 - Prob. 33ECh. 12.9 - Prob. 34ECh. 12.9 - Prob. 35ECh. 12 - Prob. 1SGACh. 12 - Prob. 2SGACh. 12 - Prob. 3SGACh. 12 - Prob. 4SGACh. 12 - Prob. 5SGACh. 12 - Prob. 6SGACh. 12 - Prob. 7SGACh. 12 - Prob. 8SGACh. 12 - Prob. 9SGACh. 12 - Prob. 10SGACh. 12 - Prob. 11SGACh. 12 - Prob. 12SGACh. 12 - Prob. 13SGACh. 12 - Prob. 14SGACh. 12 - Prob. 15SGACh. 12 - Prob. 16SGACh. 12 - Prob. 17SGACh. 12 - Prob. 18SGACh. 12 - Prob. 19SGACh. 12 - Prob. 20SGACh. 12 - Prob. 21SGACh. 12 - Prob. 22SGACh. 12 - Prob. 23SGACh. 12 - Prob. 24SGACh. 12 - Prob. 25SGACh. 12 - Prob. 26SGACh. 12 - Prob. 27SGACh. 12 - Prob. 28SGACh. 12 - Prob. 29SGACh. 12 - Prob. 30SGACh. 12 - Prob. 31SGACh. 12 - Prob. 32SGACh. 12 - Prob. 33SGACh. 12 - Prob. 34SGACh. 12 - Prob. 35SGACh. 12 - Prob. 36SGACh. 12 - Prob. 37SGACh. 12 - Prob. 38SGACh. 12 - Prob. 39SGACh. 12 - Prob. 40SGACh. 12 - Prob. 41SGACh. 12 - Prob. 42SGACh. 12 - Prob. 43SGACh. 12 - Prob. 44SGACh. 12 - Prob. 45SGACh. 12 - Prob. 46SGACh. 12 - Prob. 47SGACh. 12 - Prob. 48SGACh. 12 - Prob. 49SGACh. 12 - Prob. 50SGACh. 12 - Prob. 51SGACh. 12 - Prob. 52SGACh. 12 - Prob. 53SGACh. 12 - Prob. 54SGACh. 12 - Prob. 55SGACh. 12 - Prob. 56SGACh. 12 - Prob. 1SAPCh. 12 - Prob. 2SAPCh. 12 - Prob. 3SAPCh. 12 - Prob. 4SAPCh. 12 - Prob. 5SAPCh. 12 - Prob. 6SAPCh. 12 - Prob. 7SAPCh. 12 - Prob. 8SAPCh. 12 - Prob. 9SAPCh. 12 - Prob. 10SAP

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