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## Homework Statement

Use mathematical induction and Pascal's Identity to prove:

[tex]\binom{n}{0} - \binom{n}{1} + \binom{n}{2} - ... + (-1)^{k}\binom{n}{k} = (-1)^{k}\binom{n-1}{k}[/tex]

## The Attempt at a Solution

First, I guess this means something like:

[tex]\sum_{i=0}^{k}(-1)^{i}\binom{n}{i} = (-1)^{k}\binom{n-1}{k}[/tex]

But after that I'm stumped (as with any inductive proof with sums of binomials)... I can't see how my usual strategy would work. i.e. Figure out what n+1 would contribute to the left hand side, add it to the right side and work my way through algebraically.

Help with this would be very appreciated!