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Tricky Fractions

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.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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