I have already proved using the integral test that the follwing series converges sum from n=1 to infinity (6)/((5n+5)(n+2)) The answer I derived from the integral test which was a positive finite number was (-6/5)ln(2/3) or approximately 048656 I need to find the value that the above series converges to. How would I do this? Please show detailed explanations. This is the 3rd time I have asked this question. The first response was difficult to understand and the second response to showed me using the comparison test the series converges which I already knew. Is there a way to find the value the series converges to using the remainder estimate for the integral test? If so please demonstrate with detailed explanations.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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I have already proved using the integral test that the follwing series converges

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

The answer I derived from the integral test which was a positive finite number was (-6/5)ln(2/3) or approximately 048656

I need to find the value that the above series converges to. How would I do this? Please show detailed explanations. This is the 3rd time I have asked this question. The first response was difficult to understand and the second response to showed me using the comparison test the series converges which I already knew.

Is there a way to find the value the series converges to using the remainder estimate for the integral test? If so please demonstrate with detailed explanations.

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