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Math Help - Findind limits as x approaches infinity

  1. #1
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    Findind limits as x approaches infinity

    (i) (1-1/n)^n I have found that the limit is 1/e but cannot show why

    (ii) (1 + 1/n)^(n^2) I figure that this have something to do with e being the limit of (1 + 1/n)^n but cant see how to proceed

    (iii) (1 + 1/(n^2))^n

    (iv) Sqrt(n^2 + 2*n) - n



    Thanks in advance for any help you can provide
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  2. #2
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    Just let y=\left(1-1/n\right)^n

    Then take logs, then L'Hospitals, then convert back to y. Same with the second one.
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