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Series converge/ diverges. determine sum of series

  1. Mar 10, 2010 #1
    Determine if the series converges or diverges ad if it converges then determine the sum of the series analytically:

    infinity
    {Sigma} 2/n(n+2)
    n=1

    so i used partial fractions and got:
    {Sigma} [1/n + 1/(n+2)]

    then i used telescoping form to get the nth partial sum...
    Sn= (1/1 + 1/3) + (1/2 + 1/4) +...

    then i got the nth partial sum to be = 1+1/(n+2)

    so the series converges and its sum is 1?

    Does that seem right to everyone?
     
  2. jcsd
  3. Mar 10, 2010 #2

    Char. Limit

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    Gold Member

    First, this is in the wrong section, I believe. It should go in the homework and coursework area.

    Second, yes. However, be careful...

    As you did the work wrong, and yet got the right answer. The partial fraction decomposition for [itex]\frac{2}{(n)(n+2)}[/itex] isn't quite what you posted. Can you see the error?
     
  4. Mar 10, 2010 #3
    oh ok. i thought this was the homework and course area.

    yea its supposed to be subtraction, not addition. i got 3/2 to be the sum of the series
     
  5. Mar 10, 2010 #4

    Char. Limit

    User Avatar
    Gold Member

    There you go.

    You win...
     
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