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I am having some trouble with the following exercise:

I need to determine if the following serie converges or diverges using only the limit comparison test:

$\sum_{n=1}^{\infty} \frac{n}{(4n-3)(4n-1)}$

Please help.

Thank you in advance

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I don't know how to proceed.. – Carpediem Nov 29 '12 at 12:19
If you like an answer you could upvote it; you may want to wait a while for some possible future better answers to choose it as "the best answer", but any answer that helps you a little should be, imo, upvoted. – DonAntonio Nov 29 '12 at 12:37
up vote 1 down vote accepted


since the harmonic series diverges so does our series.

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Where did you use the limit comparison test here? – Carpediem Nov 29 '12 at 12:21
Can you explain please.. – Carpediem Nov 29 '12 at 12:25
Do you know the limit comparison test for positive series? It says: let $\,\sum a_n\,\,,\,\,\sum b_n\,$ be positive series s.t. $\,\lim\frac{a_n}{b_n}\,$ exists finitely. Then $\,\sum a_n\,$ converges iff $\,\sum b_n\,$ converges. What's not clear here? – DonAntonio Nov 29 '12 at 12:28
I understand now thank you – Carpediem Nov 29 '12 at 12:30
Any time,@user43758.... – DonAntonio Nov 29 '12 at 12:32

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