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Home » Sans chiffre : (77 − 10) = 67 → 67^12 - High Altitude Science

Sans chiffre : (77 − 10) = 67 → 67^12 - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 oxed{ ext{No finite maximum exists}}

📌 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}

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