Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Let a₁, a₂,..., anₙ, be a sequence of rational numbers. The sequence is called a Cauchy sequence if for every positive real number ε, there is a natural number N, such that for all m, n € N, m,n ≥ N ⇒ ∣aₘ−aₙ​∣ < ε.Prove that the sequence 1,1/2,1/4,1/8,....,1/2ₙ,...... is a Cauchy sequence.