Ratio Test
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- เผยแพร่เมื่อ 28 ก.ย. 2024
- This calculus 2 video tutorial provides a basic introduction into the ratio test. Examples include the ratio test with factorials, exponents, fractions, and square roots. If the limit of the ratio of next term with the previous is less than 1, the series converges. If it's more than 1, the series divergence. If the limit equals 1, the ratio test is inconclusive.
Integral Test For Divergence:
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Remainder Estimate - Integral Test:
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Limit Comparison Test:
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Alternating Series Test:
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Alternate Series Estimation Theorem:
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The Ratio Test:
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Calc 2 wasn’t too bad till chapter 11 - series lmao
What about integration??
I hate it lol
@@dremr2038 Integration is fun, just don't know how to do it though
@@Mymelodyismy123 lol , yes it is fun if you know how to use the right substitution and if you have good teacher. 😅
Idk I’m fking lovin series rn lol
@@BossKing1243 SAME DUDE. I just hated the trigonometry section
You are the reason I pass my study man. Seriously. I don't know you. But you are a living legend.
To be able to passs this section for chapter 11 calc 2
*know all the types of tests
*know when is the test applicable
*know the conditions of the test
*familiarize yourself with some examples of each test from easy to challenging level
Believe in yourself!❤
Just want to say a big thank you to The Organic Chemistry Tutor. I think this repetition style of learning is key in getting the concepts. I am learning Linear Algebra and Calculus at Uni (these are not even the advanced courses) and it is all abstract, dry and mainly focusing on definitions and theorems with very little examples.
I think that maybe because the Lecturers know this kind of stuff back to front, they probably make it harder than they might realise. Some people might understand from abstract but I learn from concrete examples and I love examples where I can practice the method
These 'series' of videos (pun intended) saved my semester lmao
You mean the “partial sums”? lol
I wish I found this channel sooner than 3 hours before my exam
ooof
rip
Same (me currently)
@@marilynjubileerose so what happened do u pass
bro i passed calculus 1 and 2 because of you, thank you for real.
Professor Organic Chemistry Tutor, thank you for another fantastic video/lecture on the classic Ratio Test in Calculus Two. This is not a difficult test to breakdown; however, the algebra could be problematic for all Calculus students. Algebra is important in all levels of Mathematics. This is an error free video/lecture on TH-cam TV with the Organic Chemistry Tutor.
We can take advantage of the two important limits to conclude that the limit is equivalent to e. The utilization of LH rule is relatively complex.
you're actually a god and thank you
Calculus wasn't this easy until I found ur channel fr
Just failed my pre calc exam😭 but this made it a lil better
Almost addicted your videos!!
true hero indeed
Absolutely phenomenal!
Life saver for days
THANK YOU SO MUCH
Saving my life brother
Our savior
What's the difference when this rule is used with a sequence?
can u explain why for the last qn, u absolute the eqn, (like when u remove the (-1)^n)
Can someone explain why he's multiplying fraction by 1/n^2 at 10:24?
@AnonymousStormChaser He is simplifying the limit equation by dividing every term but the largest nth term so that when he takes the limit it should have lots of zeros (because lim n->infinity 1/n = 0). Could also use L'Hopital's rule but this avoids derivatives.
that step in my opinion just complicates it. Since the magnitude of the numerator and denominator are both equal just use the common ration of the leading coeffiecnt
Can someone please explain as to why the (-1)^n +1 just disappears and is not useful? 24:39
The ratio test has you taking the abs. Value of the series which just negates the -1^n
Why is (n+1)! = to (n+1)n! ?
Example let n = 4
Therefore
(4+1)! = (4+1)(4!)
5! = 5(4!)
5x4x3x2x1 = 5(4x3x2x1)
120 = 120
@@nellvincervantes3223 3:03 How did he make 3^n+1 become 3^n * 3?
ratio
This Root test is wild. And I thought I was good at calculus
Bro why last problem L≠-1 and it was = 1 , i think when dividing (-1) power (n+2) by (-1) power ( n+1) the result is -1 so L=-1 ... He ignored -1 absolutely!!!
how did u get 1/e
Precalc will be the death of me, but you might've prolonged it slightly. I thank you for that.
This comment is irrelevant but I think I'm falling in love with your voice.😂
Are you allowed to assume L'hopitals rule in Calculus?
Thats what I do and still get the right answers, but you are not supposed to do that. So I’m just confused why it works.
1:14 the test is inconclusive, not the series.
Thank you very much sir...
Sounds like a tire Mark Wahlberg which is great😂
Thank-you very much
With the sum of 2^(4n+1) / n^n for n=1..inf
I didn't get 16*(1/e)*0. Although I did still end up with 0
In the intermediate steps, about 20:50 time index. I actually cancelled the n^n by noticing that (n+1)^(n+1) is just (n+1)*(n^n) so I was left with a 1/(n+1) in the denominator. Is this still a correct way of doing this?
No, because it's not true that (n+1)^(n+1) = (n+1)*(n^n). Take n=3 for example. 4^4 = 2^8 =256, but 4*(3^3) = 4*27 = 108. 256 is certainly not equal to 108, and only one counterexample is needed to disprove the notion
can someone pelase explain why he multiplied by (-n^2) at 16:50? I thought it was supposed to be 1/n^2
because -n^2 times 1/n^2 canceled each other which equal 1? if you do multiply by 1/n^2 it gonna be 1/n^4 which it doesn't cancel out!
i wonder why dont you use L.H rule there to solve the limit isn't it simpler or I am wrong i guess
Chapter 7 was crazy😭
I must be weird bc I was terrible at integrals and stuff but I can do this pretty easily
At 15:55 why does n = 1/n
if we take the abs value of our ratio and L < 1, won’t our series ABSOLUTELY converge (hence also converge)? Is this correct to imply?
Yes, the Ratio Test checks for absolute convergence;
you can also sort of use it as a Divergence Test, since L > 1 will tell you that a series diverges.
The Ratio Test is a very powerful test.
So basically you use the ratio test when you have a rational series that contains some factorial(s)?
No you use it when you fell off+ratio
u can use it when the function does not contain any constants adding in numerator or denominator, if it is added like that we can we use limit test or direct comparsion test
22:00
12:57 why is it that you could just put the n! there? i am not very familiar with factorials but that seemed like it should change the problem
@Michael DeGrave Think of 4! which is 4*3*2*1 which is also equal to (4)*3! this is the same in this case, (n+1)! is (n+1)*(n)*(n-1)*(n-2)... which is the same as (n+1)*n!
@@farlok1000 thanks for the explanation!
Does anyone know the reason behind this 24:24 ? Why disappear?
It's in the mod, so it doesn't matter whether it remains negative one or positive one depending to the value of n. it won't impact the answer as it would become positive one bcs of the mod anyways.
How could I solve the last example?
I am guessing divergence test
I couldn't understand why (-1) is not important for the last one , it also affect the result. If we use it inside of our formula, the result should have been convergent, !cause -1 is coming from the calculation of an+1 / an. I mean -1^(n+1)/ -1^(n+2) = -1 but the Professor didn't do this.
we are ssupposed to take mod of the whole thing so -1 becomes 1
im going to end it all wtf is going on
3:03 How did he make 3^n+1 become 3^n * 3?
It's an exponent rule. 3^n * 3^1= 3^n+1. When you multiply the same coefficient raised to different exponents, you just add the exponents and keep the coefficient.
@@ruthalemu7416 ty!
when you multiply you add the exponents. For example x^a.x^b=x^(a+b) so 3^n*3^1=3^(n+1). By the way, you should have written it as 3^(n+1) not 3^n+1.
@@rickybobby5584 actually 3^n/3^1 is 3^(n-1)
@@SSS20025 it was a typo... all fixed. Thanks.
Anyone else felt he should have used quotient rule when taking the derivative? Cause he changed it to a fraction
No, for L'hopital's rule you take the derivative of each part of the fraction seperately. (I made this mistake once lol)
Oh my god I think I am going to get sick
bhai mera final exam aap dey do please sir calculus me urh jaunga
23:11 I can't get 1/e, how?!
Nevermind I forgot the - symbol lmao
goat
Wishing everyone a good Calc 2 final grade
can you please take my final exam for me? I've been lost since my teacher said hi guys welcome to calc 2.
Facts
me too please
bro i felt that lmao
me rn lollll
Same I need helpppp
SERIOUSLY keep doing what you’re doing. I just ACED the hardest Calc 2 Exam just based of your videos. Thank you so much for what you do. 💗
Belated congrats girl 👏 👏 👏
Of all the people who do calculus tutorial videos, yours are the most concise and the easiest to understand. Whenever I'm scratching my head over calculus, you always seem to have the answer. Thank you for being amazing
these geometric series problems have me SHOOK.
+ L test
thank you Mark Wahlberg
L + ratio + yb better
ماشاء الله عليك كون عدنة بالوطن العربي واحد مجتهد مثلك ... ❤️
Your video is helping me thanks 🙏
These videos are 4 years old at this point but still very helpful! Thank you for showing all the steps!
5:47 you could have just done L'hopital's Rule to save time :) Great video !
that is way easier, thank you
How do we solve the last problem? I am very sad that you cut the video short. What test should we use?? I love you btw and love your teaching methods! I have learned more from you than any professor I have taken these last couple semesters. YOU ARE AMAZING!!!!
direct comparison test with p-series 1/n^1/2
or you can do alternating series test
What a wonderful set of examples! Thanks for this, great video!
got a test tomorrow wish me luck guys!
Good luck you got this 😌✅
Thanks so much! I was looking for help all yesterday cause I wasn't getting factorials and I was having a rough time on this chapter. This is one of the more helpful videos I found. Summer classes suck! Definitely feel better about my test next week now.
ratio
"get ratioed"
Too many fucking tests jesus christ almighty help me!
TH-cam no longer supports the skip button for ads.
SERIOUSLY keep doing what you’re doing. I just ACED the hardest Calc 2 Exam just based of your videos. Thank you so much for what you do.
5:31 why did you swap the n and 4**(n+1)
Thank yu so much finally got to understand ratio test💃
The factorial part was what always got me lost, glad to know there's a way to work with them.
23:16 How is he getting 1/e? Whenever I work it out, I just get e.
When you multiply by the -n^2 you should end up with ln y = -1, so y = e^-1. This can be re-written as y = 1/e. Hope that helps!
Thats because the ^n is outside of your absolute value. Just simplify it and you get 1^n/((1+1/n)^n)
@Hongki how he take n outside the modulus ? Please reply.
I had a question like this on my first exam and I got 0 and said it converges I hope I am right, because it might have also been 1 which means it inconclusive 😢 at 23:33
So for the last question that was inconclusive, would you have to find another test to prove if it converges/diverges?
Another test maybe.
I love youuuuu
at 6:16 , you said that you will multiply the top and bottom by 1/n... but WHYYY :s ???
Rashmika Babajee he just took commen denameter
Rashmika Babajee if he solved for L by plugging in ∞ for x as it was, he'd have gotten ∞/∞ which isn't helpful, so a trick to get around this is to divide each term in the problem by the highest degree of the variable which when simplified allows L to be solved for as a finite number.
Rashmika Babajee hi
@@ryanraymond321 couldnt u just use l'hopital's rule though ?
@@raichu56k yes
on 26:04, you divided the limit's numerator and denominator by 1/n, can someone explain how that happened?
he wants to get rid of inf/inf situation. What he does is the same as forcing "n" as the common denominator like this: n(1+3/n)/n(1+2/n) .
For the last problem, instead of multiplying both sides by 1/n, couldn't you just L'Hopital your way through? I'm getting the same answer that you got. Thanks
on 15:58, why we need to find derivative? is it to remove ln or is it the law?
if we directly put the limit, it becomes 0/0 form, which is indeterminate form. so we apply L'hopitals on both numerator and denominator
This part is really hard to understand, i need at least mins to solve each question when i try to do it by myself , I hate math but thank you so made this video to help me through those time
as a this video is 5 yers ago but it still live saver god bless you man
Couldn't this test be used as a Divergence Test?
It seems as if "L > 1" would serve exactly that purpose.
6:37 i really got this same answer with a different method , i can't belive that😢😢 Screw you series
11:07 if we don't simplify to this point, then the answer is 0. Because of 1/(infinity)2
These become much easier if you just memorize that the limit as n goes to infinity of [ (n+1) / n ] ^ n = e
really greatful sir... you are father of calculas,,, God bless you
Great video, as always.
Moving into third year EE soon, I passed second year which covered all this. Literally two minutes into the video and I'm wondering if I'm even supposed to understand anything I'm seeing. College is a joke
Very helpful, Thanks!
Very good videos. Hope to get an A in calc. Have an 86. Need 100s on my series retest and my final for a shout.
You deserve all my lectures' salaries
Great video 👏🏼 👏🏼
how can we set the limit equal to y?????