Answered: ollwing series converges sum from n=1…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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I used the integral test and partial fraction decomposition to demonstrate the the follwing series converges

sum from n=1 to infinity (6)/((5n+5)(n+2))

How would I show the value that it converges to? Please use detailed explanations. I had difficulty understanding the previous response to this question.

Is there a way to do this using the remainder estimate for the integral test? If so please demonstrate with detailed explanations.

Expert Solution

Step 1

Using comparison test with series

5/6 Sum(1/ n²) , the given series sum from n=1 to infinity (6)/((5n+5)(n+2)) is convergent.

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