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A friend of mine asked me to help with this problem. I tried induction, but I didn't know how to get this formula.

If $x$ and $y$ are real numbers such that $xy= ax+by$. Show that $$ x^ny^n=\sum_{k=1}^{n}{2n-1-k \choose n-1}(a^n b^{n-k}x^k+ a^{n-k}b^n y^k), \forall n \geq 0 $$

Any help is appreciated.

  • 3
    How is this related to computer science?2012-04-14
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    It is a question from "Concrete Mathematics, A Foundation for Computer Science".2012-04-14
  • 0
    I removed the ([tag:computer-science]) tag.2012-04-14
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    I'm doubtful about the validity of the equation for $n=0$, but that's a minor nitpick.2012-04-14

2 Answers 2