Example of Cauchy Sequence 1

Edit: Last term in summation at 4:30 should be 1/2^{n-1}, not 1/2^n. In the next line (top of board), the last term should be 1/2^{n-m}. Real Analysis: Let {x_n} be a sequence of real number such that |x_n - x_{n+1}| lt 1/2^n for all n gt 0. Show that {x_n} is a Cauchy sequence. We focus on basic techniques for epsilon proofs.