Does $\sum_{n=1}^{\infty} \frac{(-3/2)^n}{n}$ diverge or converge?
By the nth term test, since $\lim _{n \to \infty} \frac{(-3/2)^n}{n} \neq 0,$ I get that the series diverges.
However, I also have seen that $\sum_{n=1}^{\infty} \frac{x^n}n = \ln\big(\frac1{1-x}\big),$ so with $x=-\frac32,$ I thought the series would converge conditionally.
What am I doing wrong?