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
You can take a look at the Bertrand Series1. [Sigma n=2] 1 / (n * sqrt(ln(n))
In $\displaystyle \sum_{n=2} \frac{1}{n^a \ln^b(n)}$
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 .