Mock AIME 3 Pre 2005 Problems/Problem 15
Problem
Let denote the value of the sum
The value of can be expressed as , where and are relatively prime positive integers. Compute .
Solution
Let
Factoring the radicand, we have The fraction looks remarkably apt for a trigonometric substitution; namely, define such that . Then the RHS becomes But Therefore, This gives us So now When we sum , this sum now telescopes: Therefore, the required value giving us the desired answer of .
See Also
Mock AIME 3 Pre 2005 (Problems, Source) | ||
Preceded by Problem 14 |
Followed by Last Question | |
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