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Proving limits for converging sequences

  1. Oct 23, 2004 #1
    If a general statement like an->a where (an) is a sequence of non negative real numbers, how would we prove the sqare root an->the square root of a.

    When a=0, this can easily be done. But I don't see how this is possible from the given information for the case where a>0. Thanks for any help or suggestions.
     
  2. jcsd
  3. Oct 23, 2004 #2
    Hello

    Use the fact that ( 1+ h ) ^ n > 1 + nh (corollary). We know that the sequence (an) is non negative, hence 1 + h is positive. Work of this, and you should be able to get the desired result. Try using this corollary for an = (nth rooth of n)
     
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