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Problem with a sum of series

  1. May 18, 2006 #1
    Hi, I need to find the sum of such series:
    [tex]\sum_{n=1}^{\infty}\sin{\frac{\pi}{2^n}}[/tex]
    i know that it's sum is less than [tex]\pi[/tex] but i dont know how to find the exact value.
    thanks in advance for any help or clues
     
    Last edited: May 18, 2006
  2. jcsd
  3. May 18, 2006 #2

    NateTG

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    What have you tried doing?
     
  4. May 19, 2006 #3
    first of all i'd like to correct myself as i don't really need to find that sum. i was just wondering whether my mathematical knowledge is big[?] enough to solve this problem, so what should I have really asked about is: what method would you choose to find that sum.
    I have used the comparative criterion (precisely this inequality: [tex]sin {x}\leq x[/tex])to find out that this series is convergent and that it's sum is equal or less than [tex]\pi[/tex], but i dont know what to do next. could you tell me what is the level of difficulty of this problem? is the solution rather complicated or can it be presented in a few lines? or which mathematical terms should i know in order to solve it on my own?
     
    Last edited: May 19, 2006
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