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Finding the limit of a sequence

  1. Aug 17, 2014 #1
    1. The problem statement, all variables and given/known data

    How do you determine if the limit of (1+1/n^2)^(n^2) exists and what it is?
    This cannot use logarithms at any point.



    2. Relevant equations
    (1+1/n)^n --> e



    3. The attempt at a solution

    Let N=n^2
    Given (1+1/N)^N --> e, then (1+1/n^2)^(n^2) must --> e also.
    Is this allowed though? Do I need to put restrictions on N?
    I was thinking that I might need to show that N and n^2 have the same limit on their own, but since I have created N, it's limit is obviously that of n^2.
     
  2. jcsd
  3. Aug 17, 2014 #2

    Simon Bridge

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    Which limit do you mean?
    ... I cannot tell what the person marking you work will or will not allow. It is OK mathematically - except you need the "lim" part of the notation.
     
  4. Aug 17, 2014 #3

    HallsofIvy

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    Yes, the limit of N is the same as the limit of [itex]n^2[/itex] as n goes to infinity. And what is that limit? It's pretty obvious but you should say it.
     
  5. Aug 17, 2014 #4
    I think it would go to e.
    Thanks for your help!
     
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