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Math Help - {a_n} converges => {a_n} is Cauchy; brief question

  1. #1
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    {a_n} converges => {a_n} is Cauchy; brief question

    Prove. {a_n} converges, then it is Cauchy.

    I think I already got the answer. Can someone let me know if I'm allowed to start like this.

    |a_n - L|< e for n>N, and
    |a_m - L|< e for m>N

    |a_n - a_m| = |(a_n - L) - (a_m - L)|...
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  2. #2
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    Quote Originally Posted by cgiulz View Post
    Prove. {a_n} converges, then it is Cauchy.

    I think I already got the answer. Can someone let me know if I'm allowed to start like this.

    |a_n - L|< e for n>N, and
    |a_m - L|< e for m>N

    |a_n - a_m| = |(a_n - L) - (a_m - L)|...
    ... = |(a_n-L) + (L-a_m)| \leq |a_n-L| + |a_m - L| < \epsilon + \epsilon... yes, it is indeed correct!
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