1. Mar 24, 2007 #1

   Gib Z

   

   Homework Helper

   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?

    

   Gib Z, Mar 24, 2007
2. 
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3. Mar 24, 2007 #2

   Hurkyl

   

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   What happens if you divide by yⁿ?

    

   Hurkyl, Mar 24, 2007
4. Mar 24, 2007 #3

   Gib Z

   

   Homework Helper

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

    

   Gib Z, Mar 24, 2007
5. Mar 24, 2007 #4

   Hurkyl

   

   Staff Emeritus

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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

   Hurkyl, Mar 24, 2007
6. Mar 24, 2007 #5

   Werg22

   

   Gib Z... anyway you look at it, if you want a nice looking sum, it will only be a rearrangement of what Hurkyl proposed.

    

   Werg22, Mar 24, 2007
7. Mar 24, 2007 #6

   Gib Z

   

   Homework Helper

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

    

   Gib Z, Mar 24, 2007

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