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hampton inn & suites jekyll island jekyll island - Decision Point

📅 May 4, 2026 👤 scraface

May 04, 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}
The final answer is:
\boxed{\frac{50}{51}}

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