Prove {m/(2m+1)} is a cauchy sequence

timer Asked: Nov 24th, 2015

Question description

Prove {m/(2m+1)} is a cauchy sequence using only 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

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