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Math Help - Detrmine whthere the sequence converges

  1. #1
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    Exclamation Detrmine whthere the sequence converges

    An = 2((n+1)!) + 4^n / 2(n!)n^2

    1) determine whether it converges and if it does, find the limit of the sequence {An}

    I realise that i need to find the dominant term of the sequnece and to divide by this and so on, but i have not seen an example where (n+1)! is an element of the sequence and this has thrown me. Any help would be highly appreciated!! Limits is not my forte!

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  2. #2
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    Re: Detrmine whthere the sequence converges

    Quote Originally Posted by raggie29 View Post
    An = 2((n+1)!) + 4^n / 2(n!)n^2

    1) determine whether it converges and if it does, find the limit of the sequence {An}

    Which is it
    \frac{2(n+1)!+4^n}{2(n!)n^2}\text{ or }2(n+1)!+\frac{4^n}{2(n!)n^2}
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  3. #3
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    Re: Detrmine whthere the sequence converges

    The first one. Thanks.
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    Re: Detrmine whthere the sequence converges

    Quote Originally Posted by raggie29 View Post
    The first one. Thanks.

    Why don't you bother to use grouping symbols?
    The way you posted the expression, it actually reads as the second one.

    \frac{2(n+1)!+4^n}{2(n!)n^2}=\frac{2(n+1)+\tfrac{4  ^n}{n!}}{2n^2}

    What can you say about \left(\frac{4^n}{n!}\right)\to~?
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  5. #5
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    Re: Detrmine whthere the sequence converges

    It is of form of a basic null sequence and hence = 0?
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    Re: Detrmine whthere the sequence converges

    Quote Originally Posted by raggie29 View Post
    It is of form of a basic null sequence and hence = 0?
    So what is the overall answer?
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  7. #7
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    Re: Detrmine whthere the sequence converges

    3/2n ??
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  8. #8
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    Re: Detrmine whthere the sequence converges

    Or is it, = 0? since 1/n and 1/n^2 are both basic null sequences?
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