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I came across this excercise in an old exam (in discrete math), and I don't know how to approach it: $$\sum_{k=0}^{10}\left(\frac{1}{2}\right)^k\left(-1\right)^k\binom{10}{k}$$ I know the answer is $2^{-10}$, but I don't know why. When I was going through my text book I saw something similar regarding Catalan numbers generating functions. Thanks!

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