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Calculus 2 - Infinite Series

  1. Nov 4, 2011 #1
    This is a similar question that I have to the other one that I posted.

    Determine if the following series converges or diverges.

    sum[k=1,inf] 3/(k(k+3))

    I applied the limit comparison test with 1/k^2
    also k(k+3))=k^2+3k

    lim k->inf [ 3/(k^2+3k) ]/[ 1/k^2 ] = lim k->inf (3k^2/(k^2+3k) =H 3

    because sum[k=1,inf] 1/k^2 is a convergent p-series than sum[k=1,inf] 3/(k(k+3)) must also converge by the limit comparison test.

    I plugged this into wolfram alpha
    sum[n=1,inf] of 3/(k(k+3))
    and it said that the sum does not converge by the limit comparison test. Am I doing something wrong?

    Thanks for any help.
  2. jcsd
  3. Nov 4, 2011 #2


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    Never trust Wolfram Alpha. Reagan said "trust but verify". Plug this into WA. "sum 3/(k*(k+3)) for k from 1 to infinity". You managed to confuse the poor thing somehow. Probably the [n=1,inf] part again.
    Last edited: Nov 4, 2011
  4. Nov 4, 2011 #3

    Ray Vickson

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    Wolfram Alpha keeps giving you wrong answers (on this and some other problems). What would you conclude from that?

  5. Nov 4, 2011 #4
    Oh I screwed up the indexes. Entering that actually gives me the right answer. Thanks. You can conclude that woflram alpha isn't the be all end all super calculator.
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