Difference between revisions of "Mock AIME 3 Pre 2005 Problems/Problem 6"
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| − | + | ==Problem== | |
| − | + | Let <math>S</math> denote the value of the sum | |
<math>\sum_{n = 1}^{9800} \frac{1}{\sqrt{n + \sqrt{n^2 - 1}}}</math> | <math>\sum_{n = 1}^{9800} \frac{1}{\sqrt{n + \sqrt{n^2 - 1}}}</math> | ||
<math>S</math> can be expressed as <math>p + q \sqrt{r}</math>, where <math>p, q,</math> and <math>r</math> are positive integers and <math>r</math> is not divisible by the square of any prime. Determine <math>p + q + r</math>. | <math>S</math> can be expressed as <math>p + q \sqrt{r}</math>, where <math>p, q,</math> and <math>r</math> are positive integers and <math>r</math> is not divisible by the square of any prime. Determine <math>p + q + r</math>. | ||
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| + | == | ||
Revision as of 08:33, 14 February 2008
Problem
Let 
denote the value of the sum
can be expressed as 
, where 
and 
are positive integers and is not divisible by the square of any prime. Determine 
.
==
