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Problem #29

Mr. Garrison Prepares for the Night

Suppose that Mr Slave wants to buy n sandals s_{1}, s_{2}, s_{3}, s_{4} ... s_{n} and n dresses d_{1}, d_{2}, d_{3}, d_{4} ... d_{n}, where s_{i} is a must to have bought before buying s_{i+1} and the same with d_{i}. Let the ordered ways to add these 2n things to the girl's clothing be a(n), n varies from 1 to 60. So calculate

a(1) [(\frac{(2207 + 987\sqrt{5}}{2})^{\frac{1}{16}} + (\frac{24476 - 10946\sqrt{5}}{2})^{\frac{1}{21}}] + a(2)[(\frac{(24476 + 10946\sqrt{5}}{2})^{\frac{1}{21}} - (\frac{5778 - 2584\sqrt{5}}{2})^{\frac{1}{18}}] + a(3)[(\frac{(5778 + 2584\sqrt{5}}{2})^{\frac{1}{18}} + (\frac{76 - 34\sqrt{5}}{2})^{\frac{1}{9}}] + a(4)[(\frac{(76 + 34\sqrt{5}}{2})^{\frac{1}{9}} - (\frac{47 - 21\sqrt{5}}{2})^{\frac{1}{8}}] + ... a(60)[(\frac{(1860498 + 832040\sqrt{5}}{2})^{\frac{1}{30}} - (\frac{7881196 - 3524578\sqrt{5}}{2})^{\frac{1}{33}}]

Contributed by Mehak Gupta

Solved by 33 users

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