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Math Help - How to show that this sequence converges?

  1. #1
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    How to show that this sequence converges?

    Hi all,

    I need help to show that the following sequence converges:

    n^n/ ((n + 3)^ (n + 1))

    I can't seem to find any standard limits which can help prove that it is convergent.

    Thanks in advance,
    ArTiCk
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  2. #2
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    Quote Originally Posted by ArTiCK View Post
    Hi all,

    I need help to show that the following sequence converges:

    n^n/ ((n + 3)^ (n + 1))

    I can't seem to find any standard limits which can help prove that it is convergent.

    Thanks in advance,
    ArTiCk
    \frac{n^n}{(n+3)^{n+1}} = \frac{n^n}{(n+3)^n (n+3)} = \left(\frac{n}{n+3}\right)^n \cdot \frac{1}{n+3}<br />

    now consider the limit as n \to \infty
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