Prove cauchy sequence and thus convergence

1. Dec 14, 2011

manooba

Let (Xn) be a sequence satisfying

|Xn+1-Xn| ≤ λ^n r

Where r>0 and λ lies between (0,1). Prove that (Xn) is a Cauchy sequence and so is convergent.

2. Dec 14, 2011