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Quick series convergence question

  1. Oct 20, 2004 #1

    DE7

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    Hey all, it's been a while since I've done series and I have a quick question. How would I show the convergence or divergence of [itex]\sum \left(\sqrt{n+1}-\sqrt{n}\right)[/itex]? The ratio test is inconclusive I think, and I'm not sure how I would go about doing the root test. Or is there a series I could compare it to for the comparison test? Anyways, thanks, just need a little refresher.
     
  2. jcsd
  3. Oct 20, 2004 #2

    shmoe

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    You could try the integral comparison test. Or you could try multiplying by the conjugate, this should make the series to compare with more transparent.
     
  4. Oct 21, 2004 #3

    DE7

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    Still not sure what to do...multiplying by the conjugate gives me something that doesn't seem so helpful to me, as I still can't find a comparison series. The limit comparison tests don't seem to be working either. Any more hints please?
     
  5. Oct 21, 2004 #4

    DE7

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    Never mind...got it.
     
  6. Oct 21, 2004 #5
    Add them together you'll get f(n+1)-1, it's divergence.
     
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