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Home » From Generation 1 to Era Galactic: The Ultimate Pokémon Count Explained! - 500apps

From Generation 1 to Era Galactic: The Ultimate Pokémon Count Explained! - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 A statistician develops a new robust estimator and models its bias under repeated samples by evaluating the sum \(\sum_{k=1}^{50} \frac{1}{k(k+2)}\). Compute this sum exactly.

📌 We are to compute:

📌 \sum_{k=1}^{50} \frac{1}{k(k+2)}

📌 We use partial fraction decomposition:

📌 \frac{1}{k(k+2)} = \frac{A}{k} + \frac{B}{k+2}

📌 Multiplying both sides by \(k(k+2)\):

📌 Set \(k = 0\): \(1 = A(2) \Rightarrow A = \frac{1}{2}\)

📌 Set \(k = -2\): \(1 = B(-2) \Rightarrow B = -\frac{1}{2}\)

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