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Evaluate the limit

  1. Dec 9, 2009 #1
    1. The problem statement, all variables and given/known data

    lim.......... (1 + 1/n^2)(7/n+1)
    n->infinity




    3. The attempt at a solution

    lim.......... (1 + 1/n^2)(7/n+1)
    n->infinity

    = (7/n + 1) + (7/n^3 + n^2)

    bring out 7 because constant..

    7lim.......... (1/n + 1) + (1/n^3 + n^2)
    n->infinity
    .
    .
    .
    .
    .
    7lim.......... (n^2 + n + 1) / (n^3 + 2n^2 +n)
    n->infinity


    limit does not exist.. am i correct?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 9, 2009 #2
    Before you try to mathematically rearrange anything, try imagining what happens to (1+(1/n^2)) as n approaches infinity. Then do the same with (7/(n+1)). What do you see?
     
  4. Dec 9, 2009 #3

    Mark44

    Staff: Mentor

    No. Don't multiply the two factors. Each one has a limit that is readily obtainable. As n gets large without bound, what happens to 1/n2? What happens to 1 + 1/n2? What happens to 7/n? What happens to 7/n + 1?

    The limit does exist.
     
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