# 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

*This problem needs a solution. If you have a solution for it, please help us out by adding it.*