Difference between revisions of "2002 AIME II Problems/Problem 11"
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== Problem == | == Problem == | ||
| + | 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 12:58, 19 April 2008
Problem
Two distinct, real, infinite geometric series each have a sum of 
and have the same second term. The third term of one of the series is 
, and the second term of both series can be written in the form 
, where 
, 
, and 
are positive integers and is not divisible by the square of any prime. Find 
.
Solution
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See also
| 2002 AIME II (Problems • Answer Key • Resources) | ||
| 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 | ||
