In my textbook there is an example that shows determination whether a series converges or diverges using the limit comparison test.(adsbygoogle = window.adsbygoogle || []).push({});

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The series is (1+n *ln(n)) / (n^2 + 5)

For n large, we expect an to behave like (n*ln(n))/n^2 = (ln(n))/n, which is greater than 1/n for n>= 3, so we take bn = 1/n.

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My question is why can I use 1/n as an comparison series, I guess it's because its smaller than (ln(n))/n for large n but I'm not sure how that should validate the choice.

Could someone please explain to me?

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# Homework Help: A textbook question

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