- #1
mess1n
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Hey people, I've racked my brain on this question for hours and can't seem to get to grips with it, wondering if i could get a little guidance?
Considering the co-efficient of x^n in the expansion of (1+x)^n(1+x)^n, show:
[the sum from k=0 -> k=n of:] [nCk]2 = 2nCn
i've found the co-efficient of x^n by using the binomial expansion on (1+x)^2n, and i can see that the binomial expansion of (1+x)^2n will give a series of squared co-efficients, but I have no idea how to relate the two :s.
Any help would be much appreciated.
Cheers,
Andrew
Homework Statement
Considering the co-efficient of x^n in the expansion of (1+x)^n(1+x)^n, show:
[the sum from k=0 -> k=n of:] [nCk]2 = 2nCn
The Attempt at a Solution
i've found the co-efficient of x^n by using the binomial expansion on (1+x)^2n, and i can see that the binomial expansion of (1+x)^2n will give a series of squared co-efficients, but I have no idea how to relate the two :s.
Any help would be much appreciated.
Cheers,
Andrew