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I know it is convergent by I cannot determine why

  1. Dec 24, 2009 #1
    1. The problem statement, all variables and given/known data
    0 to infinity sum of 6/(4n-1)-6/(4n+3)
    Determine if the series is convergent or divergent.

    3. The attempt at a solution
    I know it is convergent by I cannot determine why.
     
  2. jcsd
  3. Dec 24, 2009 #2

    Dick

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    Re: Convergence

    Did you try to see if it might be a telescoping series?
     
  4. Dec 24, 2009 #3

    jgens

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    Gold Member

    Re: Convergence

    With some algebra, you should be able to show that the series converges. For example, with the particular series in question we can show that:

    [tex]\frac{6}{4n -1} - \frac{6}{4n + 3} = 6 \left(\frac{(4n + 3) - (4n - 1)}{(4n + 3)(4n - 1)}\right) = 6\left(\frac{4}{(4n + 3)(4n - 1)}\right)[/tex]

    Using a little bit more algebra, you should easily be able to determine that the series is convergent.

    Edit: Oops, somebody got here first. Sorry Dick!
     
  5. Dec 24, 2009 #4

    Dick

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    Re: Convergence

    Apologies never necessarily. Besides, you showed how a similar series would converge even if it doesn't telescope using a comparison test. That's a different answer.
     
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