Proof: Limit Law for Sum of Convergent Series | Real Analysis

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We prove the limit law for the sum of convergent series. If two series converge to a and b, then the series whose terms are the sums of the terms of the original two series is the sum of the limits: a+b. We'll prove this using the limit law for the sum of convergent sequences and the definition of a convergent series, which is based on its sequence of partial sums. #RealAnalysis

Definition of the Limit of a Convergent Series: coming soon

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Комментарии
Автор

Thanks for all your videos
Please can u do more videos on series with emphasis on things like integral test, Cauchy root test, logarithm test, D'Alembert's ratio test, comparison test, general principle of convergent and also alternating series.
Please I can't find a video where u said u were going to solve examples of finding a limit of a series using the partial sums of the series.
Thank you

ezenaboifeyinwa
Автор

Weird coincidence. I Just got to the series section of my real analysis textbook. It also had pretty much the same Proof.

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