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Math Help - limit of sequence

  1. #1
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    limit of sequence

    Could someone please show me how to prove that this limit is 0 by the squeeze/sandwich theorem in a way as simple as possible. Im not very good with all the technical math descriptions. The sequence is a=(-4)^n/n!
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  2. #2
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    Re: limit of sequence

    Since (-4)^n alternates between negative and positive, an obvious "sandwiching" will be between \frac{4^n}{n!} and -\frac{4^n}{n!}. One way to prove that \frac{4^n}{n!} goes to 0 is to show that \sum \frac{4^n}{n!} converges since a necessary condition that a series converge is that the sequence of term go to 0. You can do that by using the "ratio test" or even by noting that the series converges to e^4.
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