MathDB

Minimum upper bound on reciprocal terms of a recurrence

Source: Balkan MO ShortList 2010 A2

April 5, 2020

Problem Statement

Let the sequence

(a_n)_{n \in \mathbb{N}}

, where

\mathbb{N}

denote the set of natural numbers, is given with

a_1=2

and

a_{n+1}

=

a_n^2

-

a_n+1

. Find the minimum real number

L

, such that for every

k

\in

\mathbb{N}

\begin{align*} \sum_{i=1}^k \frac{1}{a_i} < L \end{align*}