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Math Help - Complex Limits

  1. #1
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    Complex Limits

    Find the limit of each sequence that converges; if the sequence diverges, explain why.

    (1) z_n = (\frac{1+i}{\sqrt{3}})^n

    (2) z_n = Log(1 + \frac{1}{n})

    Any help would be appreciated. Thanks!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by shadow_2145 View Post
    Find the limit of each sequence that converges; if the sequence diverges, explain why.

    (1) z_n = (\frac{1+i}{\sqrt{3}})^n

    (2) z_n = Log(1 + \frac{1}{n})

    Any help would be appreciated. Thanks!
    For (1) what is the modulus of
    \frac{1 + i}{\sqrt{3}}
    If this is greater than 1 it diverges. If it is less than 1 the limit is 0.

    For (2) what is
    \lim_{n \to \infty} log \left ( 1 + \frac{1}{n}\right )

    -Dan
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  3. #3
    Super Member 11rdc11's Avatar
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    z_n = Log(1 + \frac{1}{n})

    To see if it converges,

    \lim_{n \to \infty} Log\bigg(1 + \frac{1}{n}\bigg) = Log(1 + 0) = Log(1)

    \lim_{n \to \infty}Log(1 + \frac{1}{n}) = 0

    so it converges to 0

    Shot went to do something and came back and was too late
    Last edited by 11rdc11; September 10th 2008 at 05:07 PM. Reason: was to late
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