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Home » $ x^2 $: $ 3x^2 - 3x^2 = 0 $, - Abu Waleed Tea

$ x^2 $: $ 3x^2 - 3x^2 = 0 $, - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \sum_{k=1}^{50} rac{1}{k(k+2)}.

📌 We use partial fractions:

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

📌 Multiply both sides by $ k(k+2) $:

📌 = 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}

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