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

Thank you for the opportunity to help you with your question!

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  

 

  

Please let me know if you need any clarification. I'm always happy to answer your questions.
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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