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Home » $ f(x) = 0 $ for all $ x $ - Silent Sales Machine

$ f(x) = 0 $ for all $ x $ - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 A first-year mathematics PhD student at Yale specializes in numerical analysis for weather prediction models and is evaluating the convergence of a series related to temperature simulations. Determine the convergence of the series \(\sum_{n=1}^{\infty} rac{1}{n^2 + 3n + 2}\).

📌 First, factor the denominator:

📌 n^2 + 3n + 2 = (n + 1)(n + 2)

📌 So the general term is:

📌 a_n = rac{1}{(n + 1)(n + 2)}

📌 We apply partial fraction decomposition:

📌 rac{1}{(n + 1)(n + 2)} = rac{A}{n + 1} + rac{B}{n + 2}

📌 Multiplying both sides by \((n + 1)(n + 2)\):

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