Just as x^a-1 = (x-1)\sum_{n=0}^{a-1} x^n, is there a similar expansion for x^n - y^n?
Mar 24, 2007 #1 Gib Z Homework Helper 3,346 5 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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Mar 24, 2007 #2 Hurkyl Staff Emeritus Science Advisor Gold Member 14,916 19 What happens if you divide by yn?
Mar 24, 2007 #3 Gib Z Homework Helper 3,346 5 [tex](\frac{x}{y})^n -1[/tex] which fits the previous form, but I was hoping i'd get something a bit nicer looking >.<
[tex](\frac{x}{y})^n -1[/tex] which fits the previous form, but I was hoping i'd get something a bit nicer looking >.<
Mar 24, 2007 #4 Hurkyl Staff Emeritus Science Advisor Gold Member 14,916 19 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
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) .
Mar 24, 2007 #5 Werg22 1,425 1 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... anyway you look at it, if you want a nice looking sum, it will only be a rearrangement of what Hurkyl proposed.