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Math Help - series help

  1. #1
    Junior Member
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    series help

    the submation of 2n/(n+1)(n+2)(n+3)

    I need to find whether it converges or diverges
    Can I use the integral test for this? I am thinking of using that, would I replace the n's with x,s then find the integration and see how the limit as x goes to infinity effects the function?
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  2. #2
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    Hello, davecs77!

    \sum^{\infty}_{n=1} \frac{2n}{(n+1)(n+2)(n+3)}

    I need to find whether it converges or diverges.
    If they want simply "Converge" or "Diverge", a comparison test will suffice.


    Since . \sum \frac{2n}{(n+1)(n+2)(n+3)} \;< \;\sum \frac{2n}{n^3} \;=\;2\sum\frac{1}{n^2} .which is a convergent p-series,

    . . the given series also converges.

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