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

424 ratings | 327424 views
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Erik Moe (12 days ago)
Great video Khaner!
William Sun (7 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 (11 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)
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
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 (12 days ago)
hm?
Shaheer Imam (3 years ago)
Thank you King Khan
PoleReseal (4 years ago)
Leibniz
Dhiraj Khanal (4 years ago)