Question description
Prove {m/(2m+1)} is a cauchy sequence using the cauchy sequence definition.Cauchy sequence definition: For all epsilon > 0, there is some N in natural numbers such that if n is a natural number, then n >= N implies |a_m – a_n| < epsilon for any natural numbers n and m.Sp the proof would start with, let epsilon > 0, let N = some number, and suppose n >= N. Then|frac{n}{2n+1} – frac{m}{2m+1}| … < epsilon
