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Home » استكمالًا، لنفترض $c = 3$: - Roya Kabuki

استكمالًا، لنفترض $c = 3$: - Roya Kabuki

📅 May 8, 2026 👤 scraface

May 08, 2026

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Taking the square root of both sides:
c = \sqrt{100} = 10
Thus, the length of the hypotenuse is \(\boxed{10}\).**Question:
To compute the sum \(\sum_{k=1}^{50} \frac{1}{k(k+1)}\), we can use pa...
Multiplying through by \(k(k+1)\) gives:
= A(k+1) + Bk = Ak + A + Bk
= (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:

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