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Math Help - Series Problems

  1. #1
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    Series Problems

    Hi,

    I'm trying to determine whether a series is convergent or divergent, but I'm having some trouble testing some of the series.

    1. [Sigma n=2] 1 / (n * sqrt(ln(n))
    2. [Sigma n=1] ln(n/3n+1)

    Thanks a lot
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  2. #2
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    Quote Originally Posted by coolio View Post
    Hi,
    2. [Sigma n=1] ln(n/3n+1)

    Thanks a lot
    Hello,

    For this one, see if \lim_{n \to \infty} \ln \left(\frac{n}{3n+1} \right)=0

    See the limit of \frac{n}{3n+1}=\frac{1}{3+\frac 1n} when n tends to infinity
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  3. #3
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    1. [Sigma n=2] 1 / (n * sqrt(ln(n))
    You can take a look at the Bertrand Series

    In \sum_{n=2} \frac{1}{n^a \ln^b(n)}

    1.
    If a>1 , the Bertrand series converges regardless of the value of b or;

    If a<1 , the Bertrand series diverges regardless of the value of b or;

    If a=1 , the Bertrand series converges if and only if b>1 .
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