2008 iTest Problems/Problem 59
Problem
Let and be relatively prime positive integers such that , where the numerators always increase by , and the denominators alternate between powers of and , with exponents also increasing by for each subsequent term. Compute .
Solution
The sum can be split into two groups of numbers that we want to add: and
Let be the sum of the first sequence, so we have
Let be the sum of the second sequence, so we have That means so
See Also
2008 iTest (Problems) | ||
Preceded by: Problem 58 |
Followed by: Problem 60 | |
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