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

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Just as x^a-1 = (x-1)\sum_{n=0}^{a-1} x^n, is there a similar expansion for x^n - y^n?
 
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What happens if you divide by yn?
 
(\frac{x}{y})^n -1 which fits the previous form, but I was hoping i'd get something a bit nicer looking >.<
 
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) [/color].
 
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Gib Z... anyway you look at it, if you want a nice looking sum, it will only be a rearrangement of what Hurkyl proposed.
 
Ok i see it now, my bad lol. Thanks guys
 

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