1. The problem statement, all variables and given/known data: Prove that if xn is a sequence such that |xn - xn+1| ≤ (1/3n), for all n = 1,2,..., then it converges. 2. Relevant equations: The definition of convergence. 3. The attempt at a solution: I attempted to prove this by induction, so I am clearly far off the mark here. Any advice would be appreciated.