Difference between revisions of "2002 AIME II Problems/Problem 11"

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== Problem ==
 
== Problem ==
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Two distinct, real, infinite geometric series each have a sum of <math>1</math> and have the same second term. The third term of one of the series is <math>1/8</math>, and the second term of both series can be written in the form <math>\frac{\sqrt{m}-n}p</math>, where <math>m</math>, <math>n</math>, and <math>p</math> are positive integers and <math>m</math> is not divisible by the square of any prime. Find <math>100m+10n+p</math>.
  
 
== Solution ==
 
== Solution ==

Revision as of 13:58, 19 April 2008

Problem

Two distinct, real, infinite geometric series each have a sum of $1$ and have the same second term. The third term of one of the series is $1/8$, and the second term of both series can be written in the form $\frac{\sqrt{m}-n}p$, where $m$, $n$, and $p$ are positive integers and $m$ is not divisible by the square of any prime. Find $100m+10n+p$.

Solution

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See also

2002 AIME II (ProblemsAnswer KeyResources)
Preceded by
Problem 10
Followed by
Problem 12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions
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