Lebl-Basic-Analysis-I · Problem 2.5.10

Sequences and Series

Mathematics · series-triangle-inequality

Problem

Prove the triangle inequality for series: If ∑n=1∞xn\sum_{n=1}^{\infty} x_n converges absolutely, then ∣∑n=1∞xn∣≤∑n=1∞∣xn∣.\left| \sum_{n=1}^{\infty} x_n \right| \leq \sum_{n=1}^{\infty} |x_n|.

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