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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