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a_{n+1}=\frac{k+a_n}{1-a_n} (V Soros Olympiad 1998-99 Round 1 11.9)

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May 25, 2024
Recurrencerecurrence relationSequencealgebra

Problem Statement

The sequence of ana_n is determined by the relation an+1=k+an1−ana_{n+1}=\frac{k+a_n}{1-a_n} where k>0k > 0. It is known that a13=a1a_{13} = a_1. What values can kk take?
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