PUMaC 2024 · 代数（A 组） · 第 7 题

PUMaC 2024 — Algebra (Division A) — Problem 7

Let F = 1, F = 1, and F = F + F . Then 1 2 n +2 n +1 n ∞ X 1 1 S = arctan arctan F F n n +1 n =1 Find ⌊ 80 S ⌋ . 1 1 1 (Hint: it may be useful to note that arctan = arctan + arctan .) 1 2 3 1 2 πi/n

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