olymmath

Putnam 2020 A6

  • Session A

For a positive integer NN, let fNf_N (Corrected from FNF_N in the source.) be the function defined by fN(x)=∑n=0NN+1/2−n(N+1)(2n+1)sin⁡((2n+1)x).f_N(x) = \sum_{n=0}^N \frac{N+1/2-n}{(N+1)(2n+1)} \sin((2n+1)x). Determine the smallest constant MM such that fN(x)≤Mf_N(x) \leq M for all NN and all real xx.

Curated text Kedlaya Putnam archive. Quoted with source.

Solutions

Human solution Solution 1 by Manjul Bhargava, Kiran Kedlaya and Lenny Ng

The terms of the source let olymmath link to this solution but not copy it. Read the solution (Kedlaya Putnam archive).

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