grandes-ecoles 2022 Q4

grandes-ecoles · France · mines-ponts-maths1__psi Sequences and Series Convergence/Divergence Determination of Numerical Series

Show that $|L(z)| \leq -\ln(1-|z|)$ for all $z$ in $D$. Deduce that the series $\sum_{n \geq 1} L(z^n)$ is convergent for all $z$ in $D$.

Show that $|L(z)| \leq -\ln(1-|z|)$ for all $z$ in $D$.\\
Deduce that the series $\sum_{n \geq 1} L(z^n)$ is convergent for all $z$ in $D$.