Test the convergence of the series
Solution 1:
Correct me if wrong.
$a_n=a^{\ln(n)}; $
Rewrite: $a =e^k$, then $k=\ln(a).$
$a_n = [e^k]^{\ln(n)} =e^{k\ln(n)}$
$a_n= n^k$, where $k= \ln(a) \in \mathbb{R}.$
$\sum a^{\ln(n)}:$
1) $-1 \le k$, divergent.
4) $k\lt -1$, convergent.