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. :)

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