Let $z \in D$. Show the convergence of the series $\sum_{n \geq 1} \frac{z^n}{n}$. Specify the value of its sum when $z \in ]-1,1[$. We denote $$L(z) := \sum_{n=1}^{+\infty} \frac{z^n}{n}$$
Let $z \in D$. Show the convergence of the series $\sum_{n \geq 1} \frac{z^n}{n}$. Specify the value of its sum when $z \in ]-1,1[$. We denote
$$L(z) := \sum_{n=1}^{+\infty} \frac{z^n}{n}$$