##### Need math help to Prove that {m/(1+2m)} is a cauchy sequence.

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

Nov 24th, 2015

since

|am+1-am| = （m+1）/(3+2m）-m/(1+2m) = [(m+1)(2m+1)-(m(2m+3)]/[(2m+1)(2m+3)]

= 1/[(2m+1)(2m+3)]

as m approach infinity, the different approach 0, thus am is Cauchy sequence

Nov 24th, 2015

Could you use the definition of a cauchy sequence? 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
Nov 24th, 2015

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Nov 24th, 2015
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Nov 24th, 2015
Oct 22nd, 2017
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