Difference between revisions of "2006 SMT/Advanced Topics Problems/Problem 5"
(Created page with "==Problem== Evaluate: <math> \sum_{k=1}^{\infty}\frac{1}{k\sqrt{k+2}+(k+2)\sqrt{k}} </math> ==Solution== We try to rationalize the denominators. We have <math> \frac{1}{k\sqrt{k...") |
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Latest revision as of 20:58, 27 May 2012
Problem
Evaluate:
Solution
We try to rationalize the denominators. We have .
Now, since the denominator is factorable, we try decomposing the fraction. We have .
Finally, we have . From here, we see that everything cancels except for the and , so our final answer is .