A Very Big Problem Of Shortage Of Water

Algebra Level 1

You have a large number of friends coming over and they all get thirsty. Your first friend asks for 1/2 a cup of water. Your second friend asks for 1/4 a cup of water. Your third friend asks for 1/8 a cup of water, etc.

How many cups of water do you need to serve your friends?


The answer is 1.

Aditya Chandra by Aditya Chandra , 20, India

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3 solutions

Aditya Chandra
Jul 25, 2014

Just one. If your friends kept asking for water like this forever one cup would be enough.

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Amber Li
Aug 8, 2014

This is the sum of an infinite geometric series: 1 2 + 1 4 + 1 8 + ⋯ \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots The formula is: a 1 − r \frac{a}{1-r} where a is the first term and r is the common ratio. Here, our first term is 1/2 and the common ratio is also 1/2. So we get: 1 2 1 − 1 2 = 1 cup of water \frac{\frac{1}{2}}{1-\frac{1}{2}}=\boxed{1 \text{cup of water}}

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Raghav Raman
Aug 8, 2014

1-1/2-1/4...................................

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