Difference between revisions of "1969 Canadian MO Problems/Problem 6"
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In both cases, the expression telescopes into <math>\displaystyle (n+1)!-1.</math> | In both cases, the expression telescopes into <math>\displaystyle (n+1)!-1.</math> | ||
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* [[1969 Canadian MO Problems/Problem 5|Previous Problem]] | * [[1969 Canadian MO Problems/Problem 5|Previous Problem]] | ||
* [[1969 Canadian MO Problems/Problem 7|Next Problem]] | * [[1969 Canadian MO Problems/Problem 7|Next Problem]] | ||
* [[1969 Canadian MO Problems|Back to Exam]] | * [[1969 Canadian MO Problems|Back to Exam]] |
Revision as of 17:08, 12 October 2006
Problem
Find the sum of , where
.
Solution
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
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