I am having trouble understanding this series and its similar sequences. Considering the series in the image titled "1".  If a_n = ln(n + 1) − ln(n). Does the sequence {an}∞_n=1 converge or diverge? Additionally, considering the altered series in the image titled "2", how would I rewrite the expression by expanding the sum?  Lastly, how could I use the rewritten expression from before to show that this series diverges. Would this also be shown through the test for divergence?  Thank you, any help you can provide me with would be greatly appreciated. :)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I am having trouble understanding this series and its similar sequences. Considering the series in the image titled "1". 

If a_n = ln(n + 1) − ln(n). Does the sequence {an}∞_n=1 converge or diverge?

Additionally, considering the altered series in the image titled "2", how would I rewrite the expression by expanding the sum? 

Lastly, how could I use the rewritten expression from before to show that this series diverges. Would this also be shown through the test for divergence? 

Thank you, any help you can provide me with would be greatly appreciated. :)

00
(In(n + 1) – In(n))
n=1
Transcribed Image Text:00 (In(n + 1) – In(n)) n=1
N
SN
> (In(n + 1) – In(n))
n=1
Transcribed Image Text:N SN > (In(n + 1) – In(n)) n=1
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