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Home » All such give distinct lattice points? Not necessarily, but we count distinct \((x,y)\). - SUpost

All such give distinct lattice points? Not necessarily, but we count distinct \((x,y)\). - SUpost

📅 July 7, 2026 👤 scraface

Jul 07, 2026

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📌 The center is at $ (h, k) = (4, 3) $.

📌 Final answer: $\boxed{(4, 3)}$

📌 Question: Microfossil density $ d(t) $ in a sediment layer follows $ \sum_{k=1}^{n} \frac{1}{k(k+1)(k+2)} $. Compute this sum for $ n = 50 $.

📌 Solution: Use partial fractions to decompose $ \frac{1}{k(k+1)(k+2)} $. Let:

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

📌 Multiply through: $ 1 = A(k+1)(k+2) + Bk(k+2) + Ck(k+1) $.

📌 Solve for $ A, B, C $:

📌 For $ k = 0 $: $ 1 = A(1)(2) \implies A = \frac{1}{2} $.

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