Complex Analysis: Theory and Applications · Problem 4.1.6

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · conjugate-series-sum

Problem

Suppose that

\displaystyle\sum_{n=1}^{\infty} z_n = S

. Show that

\displaystyle\sum_{n=1}^{\infty} \overline{z_n} = \overline{S}