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Home » Vector from point on line to \(\mathbfp\): - Dachbleche24

Vector from point on line to \(\mathbfp\): - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \frac{(x - 3)^2}{\frac{88}{9}} - \frac{(y - 2)^2}{\frac{88}{16}} = 1

📌 The center of the hyperbola is \((h, k) = (3, 2)\).

📌 Therefore, the center of the hyperbola is \(\boxed{(3, 2)}\).

📌 A science policy analyst is evaluating a proposal involving the sum of a series for technological forecasting. Compute \(\sum_{n=1}^{50} \frac{1}{n(n+1)}\).

📌 The series \(\sum_{n=1}^{50} \frac{1}{n(n+1)}\) is a telescoping series. We simplify each term using partial fractions:

📌 Partial fraction decomposition:

📌 \frac{1}{n(n+1)} = \frac{1}{n} - \frac{1}{n+1}

📌 Write the series using partial fractions:

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