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Home » This is a telescoping series, where most terms cancel out: - High Altitude Science

This is a telescoping series, where most terms cancel out: - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \frac{140}{6} + c = -4 \implies \frac{70}{3} + c = -4

📌 c = -4 - \frac{70}{3} = -\frac{12}{3} - \frac{70}{3} = -\frac{82}{3}

📌 Finally, substitute \( a \), \( b \), and \( c \) into the first equation to find \( d \):

📌 -\frac{7}{6} + \frac{21}{2} - \frac{82}{3} + d = 3

📌 -\frac{7}{6} + \frac{63}{6} - \frac{164}{6} + d = 3

📌 -\frac{108}{6} + d = 3 \implies -18 + d = 3 \implies d = 21

📌 Thus, the polynomial is:

📌 f(x) = -\frac{7}{6}x^3 + \frac{21}{2}x^2 - \frac{82}{3}x + 21

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