KnowraGeometric seriesLinked fromLinked fromThe 37 pages that link to Geometric series, each with the reason it gives.All 37Broader topic 10Related 21Compared with 6Power seriesBroader topic: It supplies a basic model of power-series convergence and algebra.Infinite seriesBroader topic: Its convergence and sum follow directly from a finite partial-sum formula.Partial sumBroader topic: Its finite partial sums follow a formula that exposes dependence on the ratio.Radius of convergenceBroader topic: Its convergence condition makes the radius calculation transparent in a basic power-series example.Ratio testBroader topic: When successive term ratios approach a number below one, the series behaves like a convergent geometric series.Convergence of a seriesBroader topic: Its convergence depends sharply on whether the ratio's absolute value is less than one.Convergent seriesBroader topic: Its convergence is decided exactly by whether the ratio's absolute value is below one.Abel's theorem (power series)Broader topic: Its partial sums supply the basic weight estimates behind common proofs.Weierstrass M-testBroader topic: Geometric majorants often make the M-test easy to apply.Nth-term testBroader topic: Its terms tend to zero exactly when the ratio’s magnitude is below one, yielding convergence.