1. ## cauchy condensation test

Hello to all,
the cauchy condensation test says:
sum(a_n) converges if and only if sum (2^n)(a_(2^n)) converges.
So how do we pronve using this test the divergence of
1) sum 1/(n.lnn)
and
2) sum 1/((n)(lnn)(lnlnn))
2. From $\sum_{n=2}^{\infty} \frac{1}{n\cdot \ln n}$ the Cauchy condensation test considers $\sum_{n=2}^{\infty} \frac {2^{n}}{2^{n} \cdot \ln (2^{n})} = \sum_{n=2}^{\infty} \frac{1}{n\cdot \ln 2}$ that diverges...
From $\sum_{n=2}^{\infty} \frac{1}{n\cdot \ln n \cdot \ln (\ln n)}$ the Cauchy condensation test considers $\sum_{n=2}^{\infty} \frac {2^{n}}{2^{n} \cdot \ln (2^{n}) \cdot \ln (\ln (2^{n})} = \sum_{n=2}^{\infty} \frac{1}{n\cdot \ln 2\cdot \ln (n \cdot \ln 2)}$ that diverges...
$\chi$ $\sigma$