A First Course in Complex Analysis · Problem 7.5.17

Taylor and Laurent Series — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · series-convergence-criterion

Problem

Prove that the series ∑k≥1bk\displaystyle\sum_{k\geq 1} b_k converges if and only if lim⁡n→∞∑k≥nbk=0\displaystyle\lim_{n\to\infty} \sum_{k\geq n} b_k = 0.

Related theory

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