Alternating Series

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( • Geometric Series and the Test for Div... ) • ( • Alternating Series ) • ( • Showing a Series Diverges using Parti... ) • ( • Ratio Test to Determine if a Series C... ) • ( • Sum of an Infinite Geometric Series, ... ) • ( • P-Series ) • ( • Limit Comparison Test for Series - An... ) • In this video, we dive deep into the concept of alternating series in mathematics. We'll explore the basics of how an alternating series works, where the terms change sign from positive to negative and vice versa. This type of series can be represented in a general form with the summation notation: • ∑ (-1)^n * b_n • We will cover key examples such as: • Evaluating an alternating harmonic series: 1 - 1/2 + 1/3 - 1/4 + ... • Testing for convergence using the Alternating Series Test. • Understanding necessary conditions for an alternating series to converge: decreasing terms and a limit approaching zero. • By the end of this video, you'll have a solid understanding of how to work with alternating series, recognize convergence conditions, and solve related problems. • What You Will Learn: • The basics of alternating series and how they are structured. • The criteria for an alternating series to converge. • How to use the Alternating Series Test for evaluating convergence. • Make sure to like, share, and subscribe if you found this video helpful. Don’t forget to comment below with any questions or math topics you’d like to see in future videos! • Support me on Patreon: https://www.patreon.com/patrickjmt?ty=c • #AlternatingSeries #ConvergenceTest #Mathematics #HarmonicSeries #SeriesConvergence #InfiniteSeries #Calculus #PatrickJMT #MathHelp

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