MathDB

3

Part of 1993 Dutch Mathematical Olympiad

Problems(1)

sequence

Source: Netherlands 1993

6/28/2009
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≥2 n \ge 2. Prove that lim⁡n→∞un \displaystyle\lim_{n\to\infty}u_n exists and express its value in terms of a a and b b.
limitalgebrapolynomial