Difference between revisions of "2005 AIME II Problems/Problem 3"
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== Problem == | == Problem == | ||
| − | + | An infinite geometric series has sum 2005. A new series, obtained by squaring each term of the original series, has 10 times the sum of the original series. The common ratio of the original series is <math> \frac mn </math> where <math> m </math> and <math> n </math> are relatively prime integers. Find <math> m+n. </math> | |
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== Solution == | == Solution == | ||
== See Also == | == See Also == | ||
*[[2005 AIME II Problems]] | *[[2005 AIME II Problems]] | ||
Revision as of 22:19, 8 July 2006
Problem
An infinite geometric series has sum 2005. A new series, obtained by squaring each term of the original series, has 10 times the sum of the original series. The common ratio of the original series is 
where 
and 
are relatively prime integers. Find 
