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Math Help - Limits

  1. #1
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    Limits

    Given that (1+1/n)^n \rightarrow e as  n \rightarrow \infty, show that (1+1/n)^{n+1} \rightarrow e as  n \rightarrow \infty. Note: May use theorems containing sums, products, or quotients of convergent sequences.
    Last edited by Zocken; April 28th 2009 at 05:34 PM.
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  2. #2
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    Quote Originally Posted by Zocken View Post

    Given that (1+1/n)^n \rightarrow \infty, show that (1+1/n)^{n+1} \rightarrow e as  n \rightarrow \infty. Note: May use theorems containing sums, products, or quotients of convergent sequences.
    there's something very wrong with this problem! are you sure you wrote the question correctly? (check the problem carefully!)
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  3. #3
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    mixed up the first part. fixed now.
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  4. #4
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    Quote Originally Posted by Zocken View Post
    mixed up the first part. fixed now.
    (1 + 1/n)^{n+1}=(1+1/n)^n (1+1/n) and we know (1+1/n)^n \to e and 1 + 1/n \to 1, as n \to \infty. so the result follows.
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