Difference between revisions of "2002 AIME I Problems/Problem 4"
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== Problem == | == Problem == | ||
Consider the sequence defined by <math>a_k =\dfrac{1}{k^2+k}</math> for <math>k\geq 1</math>. Given that <math>a_m+a_{m+1}+\cdots+a_{n-1}=\dfrac{1}{29}</math>, for positive integers <math>m</math> and <math>n</math> with <math>m<n</math>, find <math>m+n</math>. | Consider the sequence defined by <math>a_k =\dfrac{1}{k^2+k}</math> for <math>k\geq 1</math>. Given that <math>a_m+a_{m+1}+\cdots+a_{n-1}=\dfrac{1}{29}</math>, for positive integers <math>m</math> and <math>n</math> with <math>m<n</math>, find <math>m+n</math>. | ||
Revision as of 13:25, 13 November 2007
Problem
Consider the sequence defined by 
for 
. Given that 
, for positive integers 
and 
with 
, find 
.
Solution
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