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

[Gib Z]

Just as $$x^a-1 = (x-1)\sum_{n=0}^{a-1} x^n$$, is there a similar expansion for x^n - y^n?

 

[Hurkyl]

What happens if you divide by yⁿ?

 

[Gib Z]

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

 

[Hurkyl]

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) .

 

[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.

 

[Gib Z]

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