Difference between revisions of "2006 SMT/Algebra Problems/Problem 8"
(Created page with "==Problem== Evaluate: <cmath> \sum_{x=2}^{10}\frac{2}{x(x^2-1)}. </cmath> ==Solution== Since the denominator of the fraction is factorable, we try partial fraction decompositio...") |
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Latest revision as of 09:52, 28 May 2012
Problem
Evaluate:
Solution
Since the denominator of the fraction is factorable, we try partial fraction decomposition. Let . Therefore, . Plugging in and , we find that .
Thus, . Expanding, we find that this is equal to
.
We now see that everything cancels (two s cancel with one ) except for a and in the beginning, and a , and in the end.
Therefore, our final answer is .