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Difference between revisions of "AoPS Wiki talk:Problem of the Day/June 22, 2011"

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==Solutions==
 
==Solutions==
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The total volume can be expressed as the sum of an infinite geometric sequence where the common ratio is <math>(\frac{5}{7})^3</math>=<math>\frac{125}{343}</math>.
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Using the formula for the sum of an infinite geometric sequence, <math>\frac{a}{1-r}</math>, where <math>a</math> is the first term, and <math>r</math> is the common ratio, we have <math>\frac{27}{1-\frac{125}{343}}</math>.
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That simplifies to <math>\boxed{\frac{9261}{218}}</math>, which is the volume.

Latest revision as of 19:02, 22 June 2011

Problem

AoPSWiki:Problem of the Day/June 22, 2011

Solutions

The total volume can be expressed as the sum of an infinite geometric sequence where the common ratio is $(\frac{5}{7})^3$=$\frac{125}{343}$.

Using the formula for the sum of an infinite geometric sequence, $\frac{a}{1-r}$, where $a$ is the first term, and $r$ is the common ratio, we have $\frac{27}{1-\frac{125}{343}}$.

That simplifies to $\boxed{\frac{9261}{218}}$, which is the volume.

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