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Math Help - urgent assignment question limit

  1. #1
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    Angry urgent assignment question limit

    lim [ ((1+5/n)^n) / e^5 ] ^n hint: use lny
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by david-david View Post
    lim [ ((1+5/n)^n) / e^5 ] ^n hint: use lny
    Im assuming n is going to infinity. And I think you have a typo. As it is we have

    \lim_{n\to\infty}\left(\frac{\left(1+\frac{5}{n}\r  ight)^n}{e^5}\right)^n

    Is that correct?
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  3. #3
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    yes thats correct, can u solve it please
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  4. #4
    Junior Member toraj58's Avatar
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    Taking into consideration that we have:

    \color{blue}\boxed{\lim_{n \to \infty} \left(1+\frac {a}{n}\right)^{bn} = e^{ab}}

    so we have:

    \lim_{n\to\infty}\left(\frac{\left(1+\frac{5}{n}\r  ight)^n}{e^5}\right)^n=\lim_{n\to\infty}\left(\fra  c{e^5}{e^5}\right)^n = 1
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  5. #5
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    thats wrong
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