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Putnam 2020 A6

Source: 81st William Lowell Putnam Competition

February 22, 2021
PutnamPutnam 2020

Problem Statement

For a positive integer NN, let fNf_N 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\left((2n+1)x \right). Determine the smallest constant MM such that fN(x)≤Mf_N (x)\le M for all NN and all real xx.
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