Along the real number line a particle starts at the

Question

Along the real number line, a particle starts at the position x₁ = 1, then its subsequent positions are programmed to be xn = 1 - exn-1 for all n ≥ 2, where ε is some positivbe number less than 1. What is the particle's limit position on the real line? In other words, what is lim_n→∞ x_n?