MathDB
x_{n+1} = x_n + b \sin x_n

Source: 39-th Vietnamese Mathematical Olympiad 2001

March 19, 2007
trigonometryintegrationcalculuscalculus computations

Problem Statement

For real a,ba, b define the sequence x0,x1,x2,...x_{0}, x_{1}, x_{2}, ... by x0=a,xn+1=xn+bsin⁡xnx_{0}= a, x_{n+1}= x_{n}+b \sin x_{n}. If b=1b = 1, show that the sequence converges to a finite limit for all aa. If b>2b > 2, show that the sequence diverges for some aa.
Back to ProblemsView on AoPS