SOLUTION: Can someone, please, explain why this equation is true? {{{sum( (-1)^k * (matrix (2, 1, n, k)), k=0, n) = 0}}} I intuitively understand why it works for odd n (as combination

Question 56961: Can someone, please, explain why this equation is true?

I intuitively understand why it works for odd n (as combinations with k elements are as many as combinations with n-k elements and they just cancel each other out in the end). But this doesn't explain the equation for even n.
Thanks!
Found 2 solutions by stanbon, fanks:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Sure it does 8C6=8C(8-6).
The evens "add" out also.
Try it for a small n like n=8 and
see what it looks like.
Cheers.
Stan H.
Answer by fanks(6) (Show Source): You can put this solution on YOUR website!
Thanks for the reply, Stan!
However, they don't cancel each out, as, for example, both and would have a plus sign in that sum ( and ).
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