x_(n+2) = 2^(-x_n) + 0.5
Source: Vietnam MO 2008, Problem 4
August 26, 2008
limitalgebra unsolvedalgebra
Problem Statement
he sequence of real number is defined by x_1 \equal{} 0, x_2 \equal{} 2 and x_{n\plus{}2} \equal{} 2^{\minus{}x_n} \plus{} \frac{1}{2} \forall n \equal{} 1,2,3 \ldots Prove that the sequence has a limit as approaches \plus{}\infty. Determine the limit.