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Home » Set up the equation for 50% alcohol: - Moon Smoking

Set up the equation for 50% alcohol: - Moon Smoking

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 For the equation to hold for all \(k\), we set up the system:

📌 A + B = 0 \quad \text{and} \quad A = 1

📌 Solving this, we find \(A = 1\) and \(B = -1\). Thus:

📌 Now, substitute this into the sum:

📌 This is a telescoping series, where most terms cancel out:

📌 After cancellation, we are left with:

📌 Thus, the sum is:

📌 - \frac{1}{51} = \frac{51}{51} - \frac{1}{51} = \frac{50}{51}

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