MathDB

Recursive sequence with square roots

Source: Baltic Way 2020, Problem 1

November 14, 2020

Inequalityalgebraalgebra proposedSequencerecursion

Problem Statement

Let

a_0>0

be a real number, and let a_n=\frac{a_{n-1}}{\sqrt{1+2020\cdot a_{n-1}^2}}, \textrm{for } n=1,2,\ldots ,2020. Show that

a_{2020}<\frac1{2020}