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Homework Help: Power series

  1. Nov 14, 2005 #1
    Hi
    I"m having truoble with fnding the power series of the following::frown:

    1+(x^3)/3+(x^6)/18+(x^9)/162+...

    Can anyone give me a hand?

    Also, any hints in finding a power series?

    Thanks !
     
  2. jcsd
  3. Nov 14, 2005 #2

    Hurkyl

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    That IS a power series...
     
  4. Nov 14, 2005 #3

    quasar987

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    Hahaha... or did you mean, you have trouble putting it into compact [itex]\sum[/itex] notation?
     
  5. Nov 14, 2005 #4

    Tide

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    I am guessing that overseastar is looking for a closed form of the sum.
     
  6. Nov 15, 2005 #5
    Looks like:

    [tex]\sum_{n=0}^{a}\frac{x^{3n}}{3^n3!}[/tex]
     
  7. Nov 15, 2005 #6

    Why do you use the factorial when 3 ! = 6 which is constant ?
     
  8. Nov 15, 2005 #7
    That fails to work when the denominator is 3.
     
  9. Nov 15, 2005 #8
    I think he means [tex]\sum_{n=0}^{\infty}\frac{x^{3n}}{3^nn!}[/tex]
     
  10. Nov 15, 2005 #9
    Thankyou Moo Of Doom, that is what I meant to write.
     
  11. Nov 16, 2005 #10

    HallsofIvy

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    And [tex]\sum_{n=0}^{\infty}\frac{x^{3n}}{3^nn!}[/tex]
    is equal to
    [tex]\sum_{n=0}^{\infty}\frac{1}{n!}\left(\frac{x^3}{3}\right)^n[/tex]
    Anyone recognize THAT??
     
  12. Nov 16, 2005 #11
    No I don't, please enlighten me.
     
  13. Nov 16, 2005 #12
    [tex]\sum_{n=0}^{\infty}\frac{1}{n!}\left(\frac{x^3}{3}\right)^n=\exp{\left(\frac{x^3}{3}\right)}[/tex]
     
  14. Nov 19, 2005 #13
    oh wow, yes, that's what i meant, sorry
     
  15. Nov 19, 2005 #14
    And thank you for all your help !
     
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