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Proof of a limit homework

  1. Oct 26, 2014 #1
    1. The problem statement, all variables and given/known data
    I have given the statements: ##a_{n}^2 \ge x## , ##a_{n+1} \le a_{n}## , ##x > 0## and ##\inf a_{n} > 0 ##. How to prove the following: ##\lim_{n \to \infty}a_{n}=\sqrt{x}##





    2. Relevant equations
    ##a_{n}^2 \ge x## , ##a_{n+1} \le a_{n}## , ##x > 0## and ##\inf a_{n} > 0 ##
    ##\lim_{n \to \infty}a_{n}=\sqrt{x}##

    3. The attempt at a solution
    I have come so far: $$a_{n}\ge a_{n+1} \ge \sqrt{x}$$ How shall I continue?
     
  2. jcsd
  3. Oct 26, 2014 #2

    PeroK

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    Are you sure that's the problem? There's not enough information there to show that the limit is ##\sqrt{x}##
     
  4. Oct 26, 2014 #3

    HallsofIvy

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    You can't prove this, it is not true!

    For example, a decreasing sequence that converges to [itex]\sqrt{x+ 1}[/itex] will satisfy all the hypotheses of your "theorem".
     
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