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Thread: state whether the sequence converges

  1. #1
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    state whether the sequence converges

    as n --> infinity, if it does, find the limit

    $\displaystyle ln(n+1)/n$ I know that $\displaystyle ln n/n --> 0$


    $\displaystyle x^{100n}/n!$ I know that $\displaystyle x^n/n! --> 0$
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  2. #2
    Member Miss's Avatar
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    Quote Originally Posted by wopashui View Post
    as n --> infinity, if it does, find the limit

    $\displaystyle ln(n+1)/n$ I know that $\displaystyle ln n/n --> 0$
    Use L'Hospital's Rule.

    $\displaystyle x^{100n}/n!$ I know that $\displaystyle x^n/n! --> 0$
    Test the convergence of $\displaystyle \sum \frac{x^{100n}}{n!}$. you should know that if $\displaystyle \sum a_n$ converges, then $\displaystyle a_n \rightarrow 0 \,\ as \,\ n\rightarrow\infty$.
    Ratio test is the best choice for this one.
    ..
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  3. #3
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    Quote Originally Posted by Miss View Post
    ..
    we have not cover the Ratio test , can we just use the property of limit of sequence to slove it?
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