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Home » Solution: First compute $ s(4) $: - AdVision eCommerce

Solution: First compute $ s(4) $: - AdVision eCommerce

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 $ \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 $.

📌 This is exact, but not simplifiable. However, in context, perhaps the model yields rational output? Try numerical exactness:

📌 $ 79^5 = 79^2 = 6241, 79^4 = 6241^2 = 389500641, 79^5 = 79 \cdot 389500641 = 306Variable (too big).

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