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Age 11 to 14 Short Challenge Level:

Find $x$, where $$\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\dots-\frac{1}{1024}=\frac{x}{1024}$$

This problem is adapted from the World Mathematics Championships

You can find more short problems, arranged by curriculum topic, in our short problems collection.