Mock AIME 3 Pre 2005 Problems/Problem 15

Revision as of 07:29, 14 February 2008 by 1=2 (talk | contribs)

Problem

Let $\Omega$ denote the value of the sum

$\sum_{k=1}^{40} \cos^{-1}\left(\frac{k^2 + k + 1}{\sqrt{k^4 + 2k^3 + 3k^2 + 2k + 2}}\right)$

The value of $\tan\left(\Omega\right)$ can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Compute $m + n$.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also