Intelligent Math Puzzle – Challenge 84

This math challenge requires basic math knowledge and some kind of logic and creative thinking to solve. Let's challenge your brain!

Challenge:

What is the sum of all fractions?
$$\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + … + \frac{1}{512} + \frac{1}{1024} =$$

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The correct answer is $$\frac{1023}{1024}$$.

$$\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + … + \frac{1}{512} + \frac{1}{1024} =$$
To add the fractions, we need to find the common denominator.
The common denominator is 1024. Therefore:
$$\frac{512}{1024} +\frac{ 256}{1024} + \frac{128}{1024} + … + \frac{2}{1024} + \frac{1}{1024} =$$
$$\frac{512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 }{1024} =\frac{1023}{1024}$$

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