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LOOK HERE: Analysis

  1. Dec 4, 2008 #1
    1. The problem statement, all variables and given/known data
    Let X be a normed linear space. Prove that X is complete if and only if [tex]\sum^{\infty}_{n=1} x_{n}[/tex] converges in X for all sequences ([tex]x_{n}[/tex]) that satisfy [tex]\sum^{\infty}_{n=1} \left\|x_{n}\right\|[/tex]< [tex]\infty[/tex]
  2. jcsd
  3. Dec 5, 2008 #2


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    What have you tried? This is actually a familiar fact from calculus. Do you remember how in R a series converged if it converged absolutely? And do you remember how that was proved? Same proof works here.
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