Northeastern WOOTers Mock AIME I Problems/Problem 14
Consider three infinite sequences of real numbers: It is known that, for all integers , the following statement holds: The elements of are defined by the relation . Let Then, can be represented as a fraction , where and are relatively prime positive integers. Find .
From the given condition, we have:
Then the sum becomes:
The final step is to take iterative differences, like so:
Almost done. Now that the numerators are constants instead of cubics , we can apply the formula for the sum of an infinite geometric series to get:
Then our answer is .