MathDB

sequence

Source: Netherlands 1993

June 28, 2009

limitalgebrapolynomial

Problem Statement

A sequence of numbers is defined by u_1\equal{}a, u_2\equal{}b and u_{n\plus{}1}\equal{}\frac{u_n\plus{}u_{n\minus{}1}}{2} for

n \ge 2

. Prove that

\displaystyle\lim_{n\to\infty}u_n

exists and express its value in terms of

a

and

b