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2023 SSMO Relay Round 1 Problems/Problem 2

Problem

Let $T=$ TNYWR. Let $a_0 = 3, a_1 = 1, a_2 = N$, and let $a_n = a_{n-1} - \frac{a_{n-3}}{8}$. Find \[\sum_{i=0}^\infty a_i.\]

Solution

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