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Home » 3) Mercenaries in Action: Why Every Secret Conflict Needs Them – Are You Ready? - ECD Germany

3) Mercenaries in Action: Why Every Secret Conflict Needs Them – Are You Ready? - ECD Germany

📅 May 12, 2026 👤 scraface

May 12, 2026

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📌 with equality if and only if \( a = b = c \). Since \( a + b + c = 1 \), equality occurs when \( a = b = c = \frac{1}{3} \). Substituting, each term becomes:

📌 \frac{\frac{1}{3}}{1 - \frac{1}{3}} = \frac{\frac{1}{3}}{\frac{2}{3}} = \frac{1}{2}

📌 So the sum is \( 3 \cdot \frac{1}{2} = \frac{3}{2} \).

📌 Thus, the minimum value is \( \boxed{\frac{3}{2}} \).

📌 Question: Compute \( \sum_{n=1}^{50} \frac{1}{\sqrt{n} + \sqrt{n+1}} \).

📌 Solution: Consider the general term:

📌 \frac{1}{\sqrt{n} + \sqrt{n+1}}

📌 Rationalize the denominator by multiplying numerator and denominator by \( \sqrt{n+1} - \sqrt{n} \):

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