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Math Help - How to find this limit?

  1. #1
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    How to find this limit?

    lim((n-1)/n)^n,n->+inf)
    calculator gives me e^-1 bt I don't know how.
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  2. #2
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    Quote Originally Posted by ninano1205 View Post
    lim((n-1)/n)^n,n->+inf)
    calculator gives me e^-1 bt I don't know how.
    Notice that \tfrac{n-1}{n} = 1 - \tfrac{1}{n}.

    You should know that \left( 1 + \tfrac{1}{n} \right)^n \to e, in general \left( 1+\tfrac{k}{n} \right)^n \to e^k.
    Therefore, \left( 1 - \tfrac{1}{n} \right)^n \to e^{-1}.
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  3. #3
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    calculus

    Which part of calculus should I study if I don't know this?
    , .
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