1960 AHSME Problems/Problem 8
Problem
The number can be written as a fraction. When reduced to lowest terms the sum of the numerator and denominator of this fraction is:
Solution
Solution 1
Let , so
The sum of the numerator and the denominator is , so the answer is .
Solution 2
The number can also be written as This is really two infinite series -- one with first term and common difference and one with first term and common difference . Apply the infinite series formula on both series.
The sum of the numerator and the denominator is , so the answer is .
See Also
1960 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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