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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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    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.2012-11-29

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$\lim_{n\to\infty}\frac{\frac{n}{(4n-3)(4n-1)}}{\frac{1}{n}}=\lim_{n\to\infty}\frac{n^2}{16n^2-16n+3}=\frac{1}{16}\Longrightarrow$

since the harmonic series diverges so does our series.

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    Yup, that is what that test, and I, said.2012-11-29