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Putnam 1952 B7

Source: Putnam 1952

July 7, 2022
PutnamtrigonometrycosineConvergence

Problem Statement

Given any real number N0,N_0, if Nj+1=cos⁡Nj,N_{j+1}= \cos N_j , prove that lim⁡j→∞Nj\lim_{j\to \infty} N_j exists and is independent of N0.N_0.
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