2008 Mock ARML 2 Problems/Problem 8
Given that and for all non-negative integers , evaluate .
The motivating factor for this solution is the form of the first summation, which might remind us of the expansion of the coefficients of the product of two polynomials (or generating functions).
Let be an arbitrary number; note that
By the given, the coefficients on the right-hand side are all equal to , yielding the geometric series:
For , this becomes , and the answer is .
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