1969 Canadian MO Problems/Problem 6
Find the sum of , where .
Note that for any positive integer Hence, pairing terms in the series will telescope most of the terms.
If is odd,
If is even, In both cases, the expression telescopes into
We need to evaluate: We replace with Distribution yields Simplifying, Which telescopes to So is the solution.
~Tomas Diaz. email@example.com
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
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