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Home » The volume \(V\) of a sphere with radius \(r\) is given by the formula: - Carbonext

The volume \(V\) of a sphere with radius \(r\) is given by the formula: - Carbonext

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 = (A + B)k + A

📌 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:

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