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Standard Form/Expansion of x^n - y^n

  1. Mar 24, 2007 #1

    Gib Z

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    Just as [tex]x^a-1 = (x-1)\sum_{n=0}^{a-1} x^n[/tex], is there a similar expansion for x^n - y^n?
     
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  3. Mar 24, 2007 #2

    Hurkyl

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    What happens if you divide by yn?
     
  4. Mar 24, 2007 #3

    Gib Z

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    [tex](\frac{x}{y})^n -1[/tex] which fits the previous form, but I was hoping i'd get something a bit nicer looking >.<
     
  5. Mar 24, 2007 #4

    Hurkyl

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    What's wrong with it? Once you're done simplifying, it's almost the same expression. Maybe you didn't multiply the y^n back in?

    I get (x - y) sum_i x^i y^(n-1-i) .
     
    Last edited: Mar 24, 2007
  6. Mar 24, 2007 #5
    Gib Z... anyway you look at it, if you want a nice looking sum, it will only be a rearrangement of what Hurkyl proposed.
     
  7. Mar 24, 2007 #6

    Gib Z

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    Ok i see it now, my bad lol. Thanks guys
     
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