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help me with a combinatorics proof?
In ti-83/84 notation, prove SUM(SEQ((N nCr K)^2,K,0,N) = (2N) nCr N
or, prove that if you take the nth row of pascals triangle, square each term, then take the sum, the result will be the nth element in row 2n
I cant come up with a method to proove it, anybody know how?
2 Answers
- ?Lv 41 decade agoFavorite Answer
Divide 2n things into two groups of equal size, say n boys and n girls. You have to pick n people total.
One way of doing this is to pick i boys and n-i girls. But that's the same as picking i boys to include and i girls to exclude. The total number of ways of doing this is (nCi)^2.
Now, sum over all choices of i<=n and you get your combintorial identity.
