Complex Analysis: Theory and Applications · Problem 4.1.12

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · series-triangle-inequality

Problem

If ∑n=0∞zn\displaystyle\sum_{n=0}^{\infty} z_n converges, show that ∣∑n=0∞zn∣≤∑n=0∞∣zn∣\left|\displaystyle\sum_{n=0}^{\infty} z_n\right| \leq \displaystyle\sum_{n=0}^{\infty} |z_n|.

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