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Series sum

  1. Oct 19, 2005 #1
    Hi,
    I've come across this series and I'm not sure in which direction I should be looking to get an equation for the sum. I've tried some simple methods but have come up blank.
    [tex]\sum\limits_{n = 0}^{n - 1} {nr^n }[/tex]
    Can anyone give me a nudge in the right direction?
     
  2. jcsd
  3. Oct 19, 2005 #2

    Galileo

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    Does it look like another series you know? Can you find some way to relate the two?

    BTW: Your index is n, but you are summing to n-1. So n is doing double duty. I suppose you mean:
    [tex]\sum_{k=0}^{n-1}kr^k[/tex]
     
  4. Oct 19, 2005 #3
    Perhaps the geometric series?
     
    Last edited: Oct 19, 2005
  5. Oct 19, 2005 #4
    I can't see how to relate the two.
    The extra multiplication by k is making it difficult.
     
  6. Oct 19, 2005 #5

    Galileo

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    Okay, here's where my ignorance about the contents of a pre-calculus class may come into play, but...the terms in the geometric series have [itex]r^k[/itex]. Is there anything, some operation, you can do to each of the [itex]r^k[/itex] terms to make it look like more or less [itex]kr^k[/itex]?
     
  7. Oct 19, 2005 #6
    hmmmmmmmmmmmm
     
  8. Oct 19, 2005 #7
    I could differentiate perhaps?
    I'm not sure what operations I can use within the summation.
     
  9. Oct 19, 2005 #8

    Galileo

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    That's a good idea!
    What'd you get if you differentiate a geometric sum?
     
  10. Oct 19, 2005 #9
    Well, I worked it out from there.
    I just wasn't expecting to get any differentiation in pre-calc.
    Thanks for the help :smile:
     
  11. Oct 19, 2005 #10

    shmoe

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    You can do it without differentiation if you like. Write it as a double sum and swap order of summation. You could also think of this as writing it as a sum of geometric series (all of different lengths).
     
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