olymmath

Putnam 2019 B2

  • Session B

For all n≥1n \geq 1, let an=∑k=1n−1sin⁡((2k−1)π2n)cos⁡2((k−1)π2n)cos⁡2(kπ2n).a_n = \sum_{k=1}^{n-1} \frac{\sin \left( \frac{(2k-1)\pi}{2n} \right)}{\cos^2 \left( \frac{(k-1)\pi}{2n} \right) \cos^2 \left( \frac{k\pi}{2n} \right)}. Determine lim⁡n→∞ann3.\lim_{n \to \infty} \frac{a_n}{n^3}.

Curated text Kedlaya Putnam archive. Quoted with source.

Solutions

Human solution Solution 1 by Kiran Kedlaya and Lenny Ng

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