MathDB
x_1=a,x_{n+1}=3x_n^3-7x_n^2+5x_n.Find the limit

Source: VietNamMO 2005,problem 6

March 11, 2005
limitinductionalgebra proposedalgebra

Problem Statement

Let {xn}\{x_n\} be a real sequence defined by: x1=a,xn+1=3xn3−7xn2+5xnx_1=a,x_{n+1}=3x_n^3-7x_n^2+5x_n For all n=1,2,3...n=1,2,3... and a is a real number. Find all aa such that {xn}\{x_n\} has finite limit when n→+∞n\to +\infty and find the finite limit in that cases.
Back to ProblemsView on AoPS