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Home » So w = 11 weeks (smallest integer greater than 10.23). - Dachbleche24

So w = 11 weeks (smallest integer greater than 10.23). - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Instead, recheck: perhaps the recurrence allows exact subtraction. But due to complexity, we evaluate:

📌 Using calculator-assisted simplification (as allowed in reasoning),

📌 $ \left(\frac{79}{160}\right)^5 \approx 0.0935 $, so $ \frac{1}{5} \times 0.0935 \approx 0.0187 $,

📌 $ c_3 \approx 0.49375 - 0.0187 = 0.47505 $, but we seek exact form.

📌 Alternatively, recognize that the problem expects symbolic evaluation. But since $ u = 79/160 $ is irrational and fifth power not simplifying, and given olympiad style, likely expects expression — but no, the sum-style suggests exact value simplifies.

📌 Wait: reconsider the function: $ s(t) = t - \frac{t^5}{5} $, and values:

📌 But we already have $ c_2 = \frac{79}{160} $

📌 Now $ c_3 = \frac{79}{160} - \frac{1}{5} \left(\frac{79}{160}\right)^5 $.

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