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Home » Thus, the ratio is \(\boxed{\frac1k^3}\). - Baxtercollege

Thus, the ratio is \(\boxed{\frac1k^3}\). - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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Using calculator-assisted simplification (as allowed in reasoning),
$ \left(\frac{79}{160}\right)^5 \approx 0.0935 $, so $ \frac{1}{5} \ti...
$ c_3 \approx 0.49375 - 0.0187 = 0.47505 $, but we seek exact form.
Alternatively, recognize that the problem expects symbolic evaluation....
Wait: reconsider the function: $ s(t) = t - \frac{t^5}{5} $, and value...
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...
$ 79^5 = 79^2 = 6241, 79^4 = 6241^2 = 389500641, 79^5 = 79 \cdot 38950...
Given olympiad style, likely the sequence stabilizes or root-finding i...

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