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Homework Help: Factorials in a series

  1. Nov 9, 2006 #1
    Ok, so here goes nothing

    I have predict what this is in series form, the factorial in the numerator is really throwing me off. I only have to do the series for the first six terms.

    C0=C0
    C2= -5/2 C0
    C4= -3/4 C2 = (5x3)/(2x4) C0
    C6= -1/6 C4 = -(5x3x1)/(2x4x6) C0

    This is what I have so far, although I cannot completely find out the numerator:

    n is 0,1,2,3
    C(2n)=[(-1)^n][???]/[(2n)!!] C0
    or
    C(2n)=[(-1)^n][???]/[2^n x n!] C0

    I cannot find out how to correctly represent the numerator. Can you guys give me any pointers?
     
  2. jcsd
  3. Nov 9, 2006 #2
    I may be missing something here, but this doesn't look like a factorial to me. It looks like [tex]\prod_{k=1}^4 \frac{2k-1}{2k}[/tex]. does it have to be in factorial form?
     
    Last edited: Nov 9, 2006
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