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Home » \[ r \approx 0.69315\% \] - AIKO, infinite ways to autonomy.

\[ r \approx 0.69315\% \] - AIKO, infinite ways to autonomy.

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 The series becomes telescoping:

📌 All intermediate terms cancel, leaving:

📌 - \frac{1}{51}

📌 = \frac{51 - 1}{51} = \frac{50}{51}

📌 Thus, the sum is \(\boxed{\frac{50}{51}}\).

📌 Question:** A renewable energy consultant is modeling the efficiency of a solar panel array with the function \( E(t) = -t^3 + 9t^2 - 24t + 20 \), where \( t \) is time in hours after sunrise. Find the time \( t \) when the rate of change of efficiency is zero.

📌 Solution:** The rate of change of efficiency is given by the derivative \( E'(t) \). Compute \( E'(t) \):

📌 E'(t) = \frac{d}{dt}(-t^3 + 9t^2 - 24t + 20) = -3t^2 + 18t - 24

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