MathDB

2020 PUMaC Individual Finals A1

Source:

January 1, 2022

algebra

Problem Statement

Let

a_1, . . . , a_{2020}

be a sequence of real numbers such that

a_1 = 2^{-2019}

, and

a^2_{n-1}a_n = a_n-a_{n-1}

. Prove that

a_{2020} <\frac{1}{2^{2019} -1}