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Disprove a convergence question

  1. Dec 5, 2008 #1
    i know that An->1

    i need to prove that (An)^n ->1

    but when i construct limit
    lim (An)^n

    the base goes to 1 and the power goes to + infinity

    that is not solvable

    i get 1^(+infinity) which says that there is no limit
    what do i do in this case in order to disprove that (An)^n->1

  2. jcsd
  3. Dec 5, 2008 #2


    Staff: Mentor

    All you need is a counterexample to show that
    [tex]\lim_{n \rightarrow \infty} (a_n)^n = 1[/tex] isn't true.

    You need a sequence {a_n} whose limit is 1 but for which the limit above isn't 1.
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