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
$$L ( z ) : = \sum _ { n = 1 } ^ { + \infty } \frac { z ^ { n } } { n }$$