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Math Help - limit

  1. #1
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    limit

    I have trouble finding the limit, some help please?
    \lim_{n \to \infty}\frac{(4n+2)n^n}{(n+1)^{n+1}}
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  2. #2
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    You need to notice that:
    \frac{{n^n }}<br />
{{\left( {n + 1} \right)^n }} = \left( {\frac{{n + 1}}<br />
{n}} \right)^{ - n}  = \left( {1 + \frac{1}<br />
{n}} \right)^{ - n}  \to \frac{1}<br />
{e}<br />
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  3. #3
    Super Member Random Variable's Avatar
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     \lim_{n \to \infty} \frac{(4n+2)n^n}{(n+1)^{n+1}} = \lim_{n \to \infty} \frac{4n+2}{n+1} \frac{n^{n}}{(n+1)^{n}}

     = \lim_{n \to \infty} \frac{4n+2}{n+1} \cdot  \lim_{n \to \infty} \frac{n^{n}}{(n+1)^{n}} = \frac{4}{e}
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