Limit comparison test | Series | AP Calculus BC | Khan Academy

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In some cases where the direct comparison test is inconclusive, we can use the limit comparison test. Learn more about it here.
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
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[@MauricioMartinez0707]

Jesus man you're fucking awesome. Theres a lot of other good teachers on youtube, like professor leonard, and partcikjmt and such, but the one thing about your teaching is that you get the point across quickly. I dont have to spend 2.5 hours watching a whole lecture, or 6-7 different videos. You give us the theorems, maybe an example here and there, in like a 6 minute video. Thanks khan academy. Ya'll know whats up

[@homelesslukeskywalker7277]

Stop swearing

[@yewut]

take my tuition

[@vee361-e1c]

Thanks a bunch!! Really well done, i understood direct comparison test but LCT flew over my head until now.

[@Anastasia231]

Thank you sir! this helped lots!

[@HighStar9821]

are there more specific requirements for bn? like if an is 1/2^n can i just set bn at 100^n?

[@walkieer]

For the second example can you use the traditional comparison test and say 1/1^n >= 1/(2^n - 1). Or is there something wrong there?

[@carlmoller807]

You're awesome dude!

[@angelakim4085]

Thank you so much !

[@tejasgajra2731]

If lim (an/bn) = t (t>1) Then an > bn ... If bn converges then it is not necessary for "an" to. Converge... Pls can you prove the theorem?

[@chaloondolaro6732]

Your voice is so calming 🤍

[@miraix6493]

thank you

[@dikshasabharwal3754]

Thanks.😄

[@rashmikababajee3328]

helloo, your tutorials are amaazzinnggg :D the only thing that I fail to understand is when do we know when to put n=1 or n=0 below the sigma notation... Can somebody please explain it to me :) Thanks in advance:)

[@haidarshehade241]

Sorry for being late but it's a given. You don't really put it. But n determines the shape of the series to determine if it's geometric or to define a mathematical function or number like eˣ or sin(x) or ln2 or whatever to be determined, which all depends on a specific n to start with.

[@yashraj4272]

Plz give homework questions at the end of your videos plzzz

[@nataliecross9403]

How do we know 1/2^n converges?

[@theerancheliyan6254]

1/2^n = 1^n/2^n = (1/2)^n and since 1/2 is greater then -1 and less then 1 it converges via geometric series. Hope this helps.

[@itecnus3490]

I like how you've got 86 subs for having a cute pic.

[@sssingh6848]

Natalie Cross Its because when u take limit as n tends to infinity then it will give a unique finite value

[@MrBoriskaful]

I dont know when to use which method AHHH my exam is on saturday

[@rafaelcrispin5519]

how'd the exam go?

[@mus1cal4ddict76]

So one use the limit comparison test when the direct comparison test gives you and inconclusive answers????

[@karlwarda7628]

In most cases

[@VickiBee]

What is this called? Calculus? The doctor treating me now says I have a tumor on the right side of my brain but that makes no sense because I've never felt pain on the right side, only on the left. He's got me all confused. I've always been left-handed and used my right brain side more than the left and now he's telling me they found a hemangioma on the right side. When you do math you use the left side of your brain, which always hurts when I use it too much. I've never felt a headache on the right side of my head, only the left. That's what makes me think is the reason I'm so lousy at math.

[@90kyro]

But (1/2^n) doesn't Converge, it Diverges and is a Harmonic Series right?

[@alaguthiagarajan4139]

it converges. as n grows larger the denominater grows exponentally from 1/2 to 1/4 to 1/8 and so on. The numbers get smaller and at infinity should approach 0. It doesn't diverge for to diverge it must be unbound and it clearly isn't for it can only grow smaller towards 0.

[@enriquerosas4510]

Harmonic series = 1/n, 1/2^n is geometric series

[@tejasgajra2731]

Nah.. It converges, actually its a geometric series with common ratio=1/2 and G.S converges if |r|

[@sangamesh2727]

[@moose7145]

But what if the limit is zero when you do lim comparison. It's not positive??

[@robertohernandez1642]

Theorem definition says it HAS to be greater than zero, so if its zero then they dont act the same, but different.

[@shayorshayorshayor]

What if the limit comparison test equals 0?

[@joshuachamblee8499]

Why did he divide the numerator and the denominator by 2^n at 5:45

[@kuaana94]

Joshua Chamblee Dividing by a fraction is the same as multiplying by its reciprocal. He had 1/2^n in the denominator so he just rearranged it to be 2^n in the numerator. This then becomes 2^n * 1/(2^n-1) so 2^n-1 ends up in the denominator. Hope that helps!

[@vee361-e1c]

I know this is old, but Joshua was asking why he divided the whole 2n/(2n-1) by 2n. It's to simplify it so it's not an indeterminate form and a finite limit can be found.

[@uduak-abasiamana9914]

what does he mean by positive and finite?

[@MrIrvydas]

+AfricannBaabeeess any number that doesn't have - in front of it, but not infinity.

[@iimousa97]

how do we choose an and bn?

[@haidarshehade241]

A positive non zero constant

[@dereksavage8728]

Thank you :_)

[@bageoop]

Khan Academy has 1 million subs and this video has 0 comments? huh

[@TheAhmadShow717]

Notification Bell 😅

[@HL-iw1du]

d

[@prabodhbharose4209]

1.25 speed