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Home » This Christmas Hack Will Reveal the Real Personality of Your Favorite Character Santa! - Crankk.io

This Christmas Hack Will Reveal the Real Personality of Your Favorite Character Santa! - Crankk.io

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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

📌 \frac{1}{k(k+1)(k+2)} = \frac{1}{2k} - \frac{1}{k+1} + \frac{1}{2(k+2)}.

📌 The sum becomes:

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

📌 Reindex the sums:

📌 = \frac{1}{2} \left( \sum_{k=1}^{50} \frac{1}{k} \right) - \left( \sum_{k=2}^{51} \frac{1}{k} \right) + \frac{1}{2} \left( \sum_{k=3}^{52} \frac{1}{k} \right).

📌 Combine terms:

📌 = \frac{1}{2} \left( 1 + \frac{1}{2} + \sum_{k=3}^{50} \frac{1}{k} \right) - \left( \frac{1}{2} + \sum_{k=3}^{50} \frac{1}{k} + \frac{1}{51} \right) + \frac{1}{2} \left( \sum_{k=3}^{50} \frac{1}{k} + \frac{1}{51} + \frac{1}{52} \right).

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