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Arithmetic operations on sequences

  1. Sep 30, 2009 #1
    1. The problem statement, all variables and given/known data

    If the sequence {a_n} n=1 to infinity converges to (a) with a_n >0 show {sqrt(a_n)}
    converges to sqrt(a)
    2. Relevant equations

    hint: conjigate first

    3. The attempt at a solution

    abs[ (a_n-a) / (sqrt(a_n)+sqrt(a) ) ] < epsilon

    i do not own LATEX, yet.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 30, 2009 #2

    Mark44

    Staff: Mentor

    You know that for some M, and for all n >= M, there is a positive epsilon such that |an - a| < epsilon.

    I would approach this by factoring |an - a| into [itex]|\sqrt{a_n} - \sqrt{a}||\sqrt{a_n} + \sqrt{a}|[/itex]. Then maybe you can replace the second factor by something clever.
     
  4. Dec 4, 2011 #3
    Clever like WHAT?!?! Waaaaah :'(
     
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