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Home » Antonym Dominate: How to Outthink and Outmatch Opponents Like Never Before! - Aurero

Antonym Dominate: How to Outthink and Outmatch Opponents Like Never Before! - Aurero

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 = A(k+2) + Bk.

📌 Set $ k = 0 $: $ 1 = A(2) \Rightarrow A = rac{1}{2} $.

📌 Set $ k = -2 $: $ 1 = B(-2) \Rightarrow B = -rac{1}{2} $.

📌 rac{1}{k(k+2)} = rac{1}{2}\left( rac{1}{k} - rac{1}{k+2}

📌 Now substitute into the sum:

📌 \sum_{k=1}^{50} rac{1}{k(k+2)} = rac{1}{2} \sum_{k=1}^{50} \left( rac{1}{k} - rac{1}{k+2}

📌 This is a telescoping series. Write out the terms:

📌 rac{1}{2} \left[ \left( rac{1}{1} - rac{1}{3}

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