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Sequences - Assumption that I need to confirm about n approaching infinity

  1. May 3, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the limit:
    an= 2n/(n2+1)1/2

    2. Relevant equations
    n/a


    3. The attempt at a solution
    Because n is approaching infinity, is it OK to disregard the +1 in the denominator and just consider the denominator to be n? This would then divide out the n in the numerator leaving 2 which is the correct answer. I think this is acceptable, but I wanted to run it by you all to confirm. Thank you in advance for your help.
     
  2. jcsd
  3. May 3, 2010 #2

    rock.freak667

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    Homework Helper

    Yes you can consider the limit like that, the '1' becomes negligible as n gets bigger and bigger.
     
  4. May 3, 2010 #3
    great, that was what I thought but I wanted to make sure that what I got and the correct answer weren't just a great coincidence. Thanks for the fast reply! :)
     
  5. May 3, 2010 #4
    factor out an n^2 in the denominator in the square root to get: sqrt((n^2)(1+(1/n^2))).

    then the problem should be something like: (2n)/[(n)(sqrt(1 + (1/n^2)))].

    Apply the properties of a limit taken to infinity and you should get 2 as your limit.

    So in essence, you could ignore the 2, but to show why you can ignore it, you can do what I just showed you.
     
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