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High School Math Calculus Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Sum of the series ∑ n = 3 ∞ 1 ( 2 n − 3 ) ( 2 n − 1 )

Sum of the series ∑ n = 3 ∞ 1 ( 2 n − 3 ) ( 2 n − 1 )

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 10, Problem 53RE

To determine

To find: Sum of the series ∑n=3∞1(2n−3)(2n−1)

Expert Solution & Answer

Answer to Problem 53RE

The sum of the given series is S=16

Explanation of Solution

Given:

The given series is,

∑n=3∞1(2n−3)(2n−1)

Calculation:

The nth term of the given series will be,

Tn=1(2n−3)(2n−1)

Using partial fraction

Tn=1(2n−3)(2n−1)=12(2n−3)−12(2n−1)

Now the partial sums will be

S1=16−110S2=(16−110)+(110−114)=16−114S3=(16−110)+(110−114)+(114−118)=16−118

In the same way

Sn=16−12(n−1)

So,

The sum of the series will be

S=limn→∞Sn=limn→∞[16−12(n−1)]⇒S=16

Therefore, the sum of the given series is S=16

Chapter 10, Problem 52RE

Chapter 10, Problem 54RE

Chapter 10 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 10.1 - Prob. 1QR Ch. 10.1 - Prob. 2QR Ch. 10.1 - Prob. 3QR Ch. 10.1 - Prob. 4QR Ch. 10.1 - Prob. 5QR Ch. 10.1 - Prob. 6QR Ch. 10.1 - Prob. 7QR Ch. 10.1 - Prob. 8QR Ch. 10.1 - Prob. 9QR Ch. 10.1 - Prob. 10QR

Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.1 - Prob. 41E Ch. 10.1 - Prob. 42E Ch. 10.1 - Prob. 43E Ch. 10.1 - Prob. 44E Ch. 10.1 - Prob. 45E Ch. 10.1 - Prob. 46E Ch. 10.1 - Prob. 47E Ch. 10.1 - Prob. 48E Ch. 10.1 - 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