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Math Help - Evaluate the limit..

  1. #1
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    Evaluate the limit..

    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?
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  2. #2
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    \displaystyle \lim_{n\rightarrow\infty}\left(1+\frac{1}{n^{2}}\r  ight)\left(\frac{7}{n}+1\right)=\lim_{n\rightarrow  \infty}\left(1+\frac{1}{n^{2}}\right)\lim_{n\right  arrow\infty}\left(\frac{7}{n}+1\right)<br />
    =\left(\lim_{n\rightarrow\infty}1+\lim_{n\rightarr  ow\infty}\frac{1}{n^{2}}\right)\left(\lim_{n\right  arrow\infty}\frac{7}{n}+\lim_{n\rightarrow\infty}1  \right)=(1+0)(0+1)=1
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  3. #3
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    Quote Originally Posted by nameck View Post
    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)

    Note that as the limit goes to infinity that
    \frac{1}{n^2} and \frac{7}{n} \to\0

    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?
    First let me ask that this does not represent a series? as you can perform a variety of test on different series to determine convergence, as the standard variable used in a series to n.

    \lim_{n\to\infty}(1+\frac{1}{n^2})(\frac{7}{n}+1)

    Note that: \frac{1}{n^2} and \frac{7}{n} \to 0

    as we goes towards infinity leaving us with 1 * 1 = 1 the limit is 1
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