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Sum of an Infinite Series

  1. Jun 20, 2011 #1
    1. The problem statement, all variables and given/known data
    (Sorry, but I haven't mastered using the sigma notation in these forums yet).

    Find the sum of the following infinite series: (n=0)^(inf) SIGMA ((pi)cos(n))/(5^n).


    2. Relevant equations
    I tried using the formula S=(a1)/(1-r).

    I know that a=pi, but I can't find "r." The equation doesn't have a consistent rate. Should I be using a different method?

    Thanks.
     
  2. jcsd
  3. Jun 20, 2011 #2

    micromass

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    Hi waealu!

    The sum you have wrote down is not a geometric series, so the formula you mentioned is not applicable (yet).

    The problem is the cos(n), that spoils the fun. But there is a way to change the cos(n) into exponents by using the formula

    [tex]\cos(n)=\frac{(e^i)^n+(e^{-i})^n}{2}[/tex]

    With this equation, you can express your series as a (sum of) geometric series.

    Note, to display the sum with LaTeX, type

    [ tex ] \sum_{n=0}^{+\infty} \frac{\pi \cos(n)}{5^n} [ /tex ]

    without the spaces in the [ tex ] tags.
     
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