MathDB

A8

Part of 2007 Balkan MO Shortlist

Problems(1)

Prove that a_1 =0 for a sequence of real numbers

Source: Balkan MO ShortList 2007 A8

4/6/2020
Let c>2c>2 and a0,a1,…a_0,a_1, \ldots be a sequence of real numbers such that \begin{align*} a_n = a_{n-1}^2 - a_{n-1} < \frac{1}{\sqrt{cn}} \end{align*} for any nn ∈\in N\mathbb{N}. Prove, a1=0a_1=0
BMOSLalgebraSequencerecurrence relation