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Does this series converge

  1. Oct 17, 2007 #1
    S=1/2+1/(2*4)+1/(2*4*6)....+1/(2*4*6..2n)+...

    I want to calculate the sum of this series, but it seems not to converge.
    Can anyone help me

    Thank you.
     
  2. jcsd
  3. Oct 17, 2007 #2

    matt grime

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    It does converge, the sum is


    [tex]\sum_{n=1}^{\infty} \frac{1}{n!2^n}[/tex]

    which is a well known series (what Taylor series do you know?).
     
  4. Oct 17, 2007 #3
    Thank you, yes it does converge. Could you please tell me how to calculate the sum.
    I should revise some old maths books.
     
  5. Oct 17, 2007 #4

    morphism

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    He did tell you how to calculate the sum:
     
  6. Oct 19, 2007 #5
    I found it myself. The Taylor expansion of e^x at 1/2. Thanks.
     
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