Difference between revisions of "1956 AHSME Problems/Problem 25"
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Revision as of 13:33, 30 April 2017
Problem 25
The sum of all numbers of the form , where takes on integral values from to is:
Solution
The sum of the odd integers from to is . However, in this problem, the sum is instead , starting at rather than . To rewrite this, we note that is less than for every we add, so for 's, we subtract , giving us ,which factors as .