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Prove lim(sqrt(a(n)^2))=a^2

  1. Sep 20, 2008 #1
    1. The problem statement, all variables and given/known data
    I am trying to prove that given an[tex]\geq[/tex]0 for all n , and
    lim(an=a), that lim(sqrt(a(n)^2))=a^2.

    2. Relevant equations

    3. The attempt at a solution
    I have multiplied the bottom and top by the conjugate but I cannot find what to set as a lower bound for the absolute value of sqrt(an)+sqrt(a).

    Please help.
  2. jcsd
  3. Sep 20, 2008 #2


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    Hi LMKIYHAQ! :smile:

    I don't get it … for an ≥ 0, sqrt(a(n)^2) = an, and so lim(sqrt(a(n)^2)) = a, doesn't it? :confused:
  4. Sep 20, 2008 #3


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    I agree with tiny-tim: whether you write it as

    \lim_{n \to \infty} \sqrt{a_n^2}


    \lim_{n \to \infty} \sqrt{a_n}^2

    the limit certainly is not [tex] a^2 [/tex].
  5. Sep 20, 2008 #4
    You mean
  6. Sep 20, 2008 #5
    Darn. I wrote the problem down wrong everybody. I am sorry, I hope you are all good enough s.t. you didn't spend much time thinking about that!! I am sorry.

    How do I delete a thread?

    P.S. i meant lim(sqrt(a(n)))=a(n), and I figured it out.
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