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Difference between revisions of "2005 AIME II Problems/Problem 11"

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== Problem ==
 
== Problem ==
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A semicircle with diameter <math>d</math> is contained in a square whose sides have length 8. Given the maximum value of <math>d</math> is <math>m-\sqrt{n}</math>, find <math>m+n</math>.
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Let <math> m </math> be a positive integer, and let <math> a_0, a_1,\ldots,a_m </math> be a sequence of integers such that <math> a_0 = 37, a_1 = 72, a_m = 0, </math> and <math> a_{k+1} = a_{k-1} - \frac 3{a_k} </math> for <math> k = 1,2,\ldots, m-1. </math> Find <math> m. </math>
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== Solution ==
 
== Solution ==
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== See Also ==
 
== See Also ==
 
*[[2005 AIME II Problems]]
 
*[[2005 AIME II Problems]]

Revision as of 23:30, 8 July 2006

Problem

Let $m$ be a positive integer, and let $a_0, a_1,\ldots,a_m$ be a sequence of integers such that $a_0 = 37, a_1 = 72, a_m = 0,$ and $a_{k+1} = a_{k-1} - \frac 3{a_k}$ for $k = 1,2,\ldots, m-1.$ Find $m.$

Solution

See Also

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