MathDB

1

Part of 2020 Baltic Way

Problems(1)

Recursive sequence with square roots

Source: Baltic Way 2020, Problem 1

11/14/2020
Let a0>0a_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 a2020<12020a_{2020}<\frac1{2020}.
Inequalityalgebraalgebra proposedSequencerecursion