Difference between revisions of "1991 AIME Problems/Problem 15"
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== Problem == | == Problem == | ||
For positive integer <math>n_{}^{}</math>, define <math>S_n^{}</math> to be the minimum value of the sum | For positive integer <math>n_{}^{}</math>, define <math>S_n^{}</math> to be the minimum value of the sum | ||
| − | + | <math>\sum_{k=1}^n \sqrt{(2k-1)^2+a_k^2},</math> | |
where <math>a_1,a_2,\ldots,a_n^{}</math> are positive real numbers whose sum is 17. There is a unique positive integer <math>n^{}_{}</math> for which <math>S_n^{}</math> is also an integer. Find this <math>n^{}_{}</math>. | where <math>a_1,a_2,\ldots,a_n^{}</math> are positive real numbers whose sum is 17. There is a unique positive integer <math>n^{}_{}</math> for which <math>S_n^{}</math> is also an integer. Find this <math>n^{}_{}</math>. | ||
Revision as of 17:32, 19 April 2007
Problem
For positive integer 
, define 
to be the minimum value of the sum
where 
are positive real numbers whose sum is 17. There is a unique positive integer 
for which is also an integer. Find this .
Solution
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See also
| 1991 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Last question | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
