# Math Help - Series Problems

1. ## 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

2. Originally Posted by coolio
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

3. 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 .