Difference between revisions of "1991 AIME Problems/Problem 15"
m |
|||
Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
+ | For positive integer <math>n_{}^{}</math>, define <math>S_n^{}</math> to be the minimum value of the sum | ||
+ | <center><math>\sum_{k=1}^n \sqrt{(2k-1)^2+a_k^2},</math></center> | ||
+ | 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>. | ||
== Solution == | == Solution == | ||
+ | {{solution}} | ||
== See also == | == See also == | ||
− | + | {{AIME box|year=1991|num-b=14|after=Last question}} |
Revision as of 02:43, 2 March 2007
Problem
For positive integer , define
to be the minimum value of the sum
![$\sum_{k=1}^n \sqrt{(2k-1)^2+a_k^2},$](http://latex.artofproblemsolving.com/1/e/9/1e96fb544379cfe35283e8fa9f7d5367624e4676.png)
where are positive real numbers whose sum is 17. There is a unique positive integer
for which
is also an integer. Find this
.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
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 |