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Math Help - a simple limit question

  1. #1
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    a simple limit question

    given a(n) = (1+2/n)^n...the answer to whether the sequence converges or diverges is e^2...how do i do this?

    secondly, the sequence given is (cos n)^2/(2^n)..how to find the limits?
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  2. #2
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    Quote Originally Posted by serenalee View Post
    given a(n) = (1+2/n)^n...the answer to whether the sequence converges or diverges is e^2...how do i do this?

    secondly, the sequence given is (cos n)^2/(2^n)..how to find the limits?
    1. \lim_{n \rightarrow + \infty} \left( 1 + \frac{x}{n} \right)^n = e^x is a well known limit.

    2. Note that \cos n is bounded ....
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