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2021 BMT Algebra Tiebreaker #1

Source:

March 10, 2024
algebra

Problem Statement

Let the sequence {an}\{a_n\} for n≥0n \ge 0 be defined as a0=ca_0 = c, and for n≥0n \ge 0, an=2an−14an−12−1.a_n =\frac{2a_{n-1}}{4a^2_{n-1} -1}. Compute the sum of all values of cc such that a2020a_{2020} exists but a2021a_{2021} does not exist.
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