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Math Help - 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

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


    x^{100n}/n! I know that 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

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

    x^{100n}/n! I know that x^n/n! --> 0
    Test the convergence of \sum \frac{x^{100n}}{n!}. you should know that if \sum a_n converges, then 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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