When a series alternates (plus, minus, plus, minus,...) there's a fairly simple way to determine whether it converges or diverges: see if the terms of the series approach 0.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-bc/bc-series/bc-ratio-alt-series/e/alternating-series?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC
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Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-series/bc-ratio-alt-series/v/ratio-test-convergence?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC
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If anyone is wondering (as I was) whether the two conditions mentioned in the video are equivalent, they're not. A +ve decreasing sequence may approach any non-negative value (not necessarily zero) as n approaches infinity. Also, a +ve sequence that approaches zero as n approaches infinity doesn't necessarily have to be decreasing (think abs(sin(n)/n)).
Can you use the Alternating series test if something is being added in the series?
like, (5^(-n) + (-2)^(n) * (3)^(-2n+1))?
If it were just (-2)^n * 3^(-2n+1) it should pass the alternating series test, but the addition is confusing me.
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