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Mike Miller wrote:
On Sat, 19 Apr 2008, Stephen Montgomery-Smith wrote:
Mike Miller wrote:
On Fri, 18 Apr 2008, Stephen Montgomery-Smith wrote:
Here is a math problem I worked on when I was a student. Show that
N
Sum (N choose i) x(x+i)^(i-1) y(y+n-i)^(n-i) = (x+y)(x+y+n)^(n-1).
i=0
Does n = N ?
Yes.
OK. So I can write it thusly:
N
Sum (N choose i) x(x+i)^(i-1) y(y+N-i)^(N-i) = (x+y)(x+y+N)^(N-1)
i=0
But now when I try N=0 or N=1, I don't get the right answer. What sets
do x, y and N come from? Maybe you typed something wrong.
Example: For N=1, I'm getting y(x+y+1) instead of x+y.
I must have typed it wrong. It should be
N
Sum (N choose i) x(x+i)^(i-1) y(y+N-i)^(N-i-1) = (x+y)(x+y+N)^(N-1)
i=0
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