Complex Analysis: Theory and Applications · Problem 4.1.9

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · series-convergence-terms-zero

Problem

Show that, if

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

converges, then

\displaystyle\lim_{n\to\infty} z_n = 0

. Hint:

z_n = S_n - S_{n-1}