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Series Expansions

  1. Jan 27, 2009 #1
    Hi there,

    I'm looking for a series that expands to look like : (pi^2)/3! - (pi^4)/5! + (pi^6)/7! - ... =1

    Any ideas would be greatly appreciated as I can't seem to get anywhere with it!

    Thanks,


    K
     
  2. jcsd
  3. Jan 27, 2009 #2

    CompuChip

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    Science Advisor
    Homework Helper

    Can you start by writing the expression as a sum, i.e.
    [tex]\pi^2 / 3! - \pi^4 / 5! + \pi^6 / 7! - \cdots = \sum_{n = n_0}^{N} a_n[/tex]

    Also, the Taylor series of the sine function
    [tex]\sum_{n = 0}^\infty (-1)^n \frac{x^{2n+1}}{(2n + 1)!} = \sin(x)[/tex]
    may come in handy.
     
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