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Putnam 2020 A3

Source: 81st William Lowell Putnam Competition

February 22, 2021
PutnamPutnam 2020college contestsreal analysis

Problem Statement

Let a0=π/2a_0=\pi /2, and let an=sin⁡(an−1)a_n=\sin (a_{n-1}) for n≥1n\ge 1. Determine whether ∑n=1∞an2 \sum_{n=1}^{\infty}a_n^2 converges.
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