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Math Help - infinity question

  1. #1
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    infinity question

    How do I show that as n\to\infty of (1-\frac{x}{\theta n})^n = e^{-\frac{x}{\theta}}??
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  2. #2
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    Is it \lim_{n \rightarrow \infty} (1+\frac{x}{n})^n?

    You can prove that the sequence has an upper bound (3) and a lower bound (2) using the binomial expansion. I guess that's where to start!
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  3. #3
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    Hello,

    Note that :

    \left(1-\frac{x}{n \theta}\right)^n=\left(\left(1-\frac{x}{n \theta}\right)^{-n\theta/x}\right)^{-x/\theta}

    Substitute \frac 1t=-\frac{x}{n \theta} and you will get :

    \lim_{t \to \infty} \left(\left(1+\frac 1t\right)^t\right)^{-x/\theta}

    and this is a known formula
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