1985 AHSME Problems/Problem 5
Problem
Which terms must be removed from the sum
if the sum of the remaining terms is to equal ?
Solution
We compute the entire sum as so the two terms to be removed must sum to . That is, for some .
Since and are coprime, we deduce that is a multiple of , so or must be a multiple of . It follows that one of them must be , and we obtain so the two terms we must remove are .
See Also
1985 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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