Difference between revisions of "1996 USAMO Problems/Problem 5"
(Created page with "'''Problem:''' ---- Prove that the average of the numbers <math> n\sin n^{\circ}\; (n = 2,4,6,\ldots,180) </math> is <math>\cot 1^\circ</math>. '''Solution:''' ---- First, ...") |
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Revision as of 10:46, 29 January 2013
Problem:
Prove that the average of the numbers is .
Solution:
First, as we omit that term. Now, we multiply by to get, after using product to sum, . This simplifies to . Since this simplifies to . We multiplied by in the beginning, so we must divide by it now, and thus the sum is just , so the average is , as desired.