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Alternating series test | Series | AP Calculus BC | Khan Academy

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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 Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-series/bc-ratio-alt-series/v/conditional-and-absolute-convergence?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC 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 AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan Academy's AP Calculus BC channel: https://www.youtube.com/channel/UC5A2DBjjUVNz8axD-90jdfQ?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
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Text Comments (24)
Erik Moe (10 days ago)
Great video Khaner!
William Sun (6 months ago)
If Bn is >=0 for all n, and the limit as n approaches infinity of Bn is 0, isn’t it a given that Bn is decreasing for all n greater than a specific N value?
Samg381 (10 months ago)
This isn't an alternating series.
Andrew6James (11 months ago)
Why does 1/n converge using the alternating series test but for the integral test the limit for 1/n as n tends towards infinity is divergent
Deva Anbu Raj (11 months ago)
Thank you so much. It was very useful.
TheHappyTrainWreck (11 months ago)
b_n > or = zero? If it's zero, wouldn't a_n also equal zero and you wouldn't have a sequence?
fenta molla (1 year ago)
so nice pls continue
fenta molla (1 year ago)
so nice pls continue
Mehrin Ali (1 year ago)
Thank you so much Mr.Khan!
jivan kharel (1 year ago)
jawed ahmadi (1 year ago)
Hey can u tell me if we have a question So how can we know that which test should we apply for the question amongst these tests plzzzzzzzz
ana majhol (2 years ago)
Let's make this comment a little bit more concrete
Paul Lee (2 years ago)
Studying for a Calc 2 Final and Bam! Khan academy saved my life. Thanks a lot Sal!
Robbie Skinner (2 years ago)
lol @ 0:00
Haitham Gad (2 years ago)
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)).
AverageBrick (1 month ago)
Thanks a lot!!!!
ZephoN (2 years ago)
Hmm, an alternating series is actually a lot easier than I thought it'd be.
Brett_Andromeda (3 years ago)
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.
pierre fabela (3 years ago)
Khanvergence :O
Erik Moe (10 days ago)
hm?
Shaheer Imam (3 years ago)
Thank you King Khan
PoleReseal (4 years ago)
Leibniz
Dhiraj Khanal (4 years ago)
Please make a video about how to get its value................ @ Khan academy
Farhan Syed (4 years ago)
First comment!

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