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Math Help - limit of a sequence

  1. #1
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    limit of a sequence

    hi,
    find the lim of |1/(((n+1)^2)*2^n)|^(1/n).

    Sorry if that's a bit messy.
    Thanks
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  2. #2
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    Quote Originally Posted by tbyou87 View Post
    hi,
    find the lim of |1/(( (n+1)^2 )*2^n)|^(1/n).

    Sorry if that's a bit messy.
    Thanks
    \lim \ \left( \frac{1}{2^n (n+1)^2} \right)^{1/n} = \lim \ \frac{1}{2(n+1)^{1/n}(n+1)^{1/n}} =  \frac{1}{2n^{1/n} \left( 1 + \frac{1}{n} \right)^{1/n} \cdot n^{1/n} \left( 1 + \frac{1}{n} \right)^{1/n} } = \frac{1}{2e^2}.
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  3. #3
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    Hi,
    When I plug in large values for n such as n=300 i get .48143 while the limit 1/2(e^2) is around .0676676.

    I am doing something wrong?
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  4. #4
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    No I am doing something wrong. I did the limit of e is (1+1/n)^n NOT (1+1/n)^{1/n}. (I had something to drink).

    But (n+1)^{1/n} \to 1 because:
    n^{1/n} \leq (n+1)^{1/n} \leq (n+n)^{1/n} = 2^{1/n} \cdot n^{1/n}.
    Use the squeze theorem.
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  5. #5
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    The limit is thus 1/2 right?
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  6. #6
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    Quote Originally Posted by tbyou87 View Post
    The limit is thus 1/2 right?
    Why you asking me? It is clear that it is 1/2.
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