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Math Help - another sequence Help please

  1. #1
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    another sequence Help please

    An= n[ln(n+1) - lnn]

    does it equal e
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by twilightstr View Post
    An= n[ln(n+1) - lnn]

    does it equal e
    It doesn't equal e...but you have the right idea.

    Note that a_n=n\left(\ln(n+1)-\ln(n)\right)=n\ln\left(\frac{n+1}{n}\right)=\ln\l  eft[\left(1+\frac{1}{n}\right)^n\right]

    Now, \lim \left(1+\frac{1}{n}\right)^n=e

    So, \lim a_n=\dots

    Does this make sense?
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