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- Опубліковано 29 бер 2018
- 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:
• Calculus 2 - Integral ...
Remainder Estimate - Integral Test:
• Remainder Estimate For...
P-Series:
• P-series
Direct Comparison Test:
• Direct Comparison Test...
Limit Comparison Test:
• Limit Comparison Test
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Alternating Series Test:
• Alternating Series Test
Alternate Series Estimation Theorem:
• Alternate Series Estim...
Absolute & Conditional Convergence:
• Absolute Convergence, ...
The Ratio Test:
• Ratio Test
The Root Test:
• Root Test
__________________________________
Series Tests - Practice Problems:
• Calculus 2 - Geometric...
Taylor & Maclaurin Polynomials:
• Taylor Polynomials & M...
Taylor's Remainder Theorem:
• Taylor's Remainder The...
Power Series - Interval Convergence:
• Power Series - Finding...
Power Series - Derivatives & Integrals:
• Power Series - Differe...
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Calculus Final Exam and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
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Wishing everyone a good Calc 2 final grade
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
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
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!❤
You are the reason I pass my study man. Seriously. I don't know you. But you are a living legend.
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
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
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.
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
What a wonderful set of examples! Thanks for this, great video!
These videos are 4 years old at this point but still very helpful! Thank you for showing all the steps!
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.
ماشاء الله عليك كون عدنة بالوطن العربي واحد مجتهد مثلك ... ❤️
Your video is helping me thanks 🙏
these geometric series problems have me SHOOK.
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 UA-cam TV with the Organic Chemistry Tutor.
The factorial part was what always got me lost, glad to know there's a way to work with them.
Great video, as always.
Absolutely phenomenal!
Very helpful, Thanks!
Almost addicted your videos!!
really greatful sir... you are father of calculas,,, God bless you
Thank yu so much finally got to understand ratio test💃
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.
got a test tomorrow wish me luck guys!
Good luck you got this 😌✅
can u explain why for the last qn, u absolute the eqn, (like when u remove the (-1)^n)
you're actually a god and thank you
Actually the best channel ever created
Great video 👏🏼 👏🏼
love your videos!
true hero indeed
THANK YOU SO MUCH
Life saver for days
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
Thank you very much sir...
You deserve all my lectures' salaries
Thank-you very much
5:47 you could have just done L'hopital's Rule to save time :) Great video !
that is way easier, thank you
9:52 would it be right to write it as ((n+1)/n)^2 ? so that we get (1+1/n)^2
Calculus wasn't this easy until I found ur channel fr
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
What's the difference when this rule is used with a sequence?
as a this video is 5 yers ago but it still live saver god bless you man
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.
So for the last question that was inconclusive, would you have to find another test to prove if it converges/diverges?
Another test maybe.
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
thank you
Just failed my pre calc exam😭 but this made it a lil better
can any tell how we know which test to use like where to use ratio test ,where to use AST or p series
Thanks again
very nice video
Is the limit as n goes to infinity of the absolute value of the quantity of (1 +1/n)^n equal to 1? Why did he have to go further than that? 14:23
Because 1^infinity is an indeterminate form....don't you think this reminds of something from calculus...
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) .
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
God bless you bruh!
why do you just move stuff from one side of the fraction to the other?
Thanks
If the problem just like the last one is inconclusive, will using other tests for convergence must be used?
Steve Amores
yeah then you need to use other tests
Thank you. This helped a lot. Didn't you omit a negative in the last question?
meant example instead of question.
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
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
Thank you sir g
My teacher is good but you are just amazing
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
5:31 why did you swap the n and 4**(n+1)
how did u get 1/e
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!
Our savior
thank you Mark Wahlberg
how did he get n! in the left denominator?
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.
Precalc will be the death of me, but you might've prolonged it slightly. I thank you for that.
How to chek for it?
(3^n+n^2)/(6^n+8^n)
UA-cam no longer supports the skip button for ads.
Hey can you explain how (n+1)! is the same as (n+1)n!?
(n+1) n (n-1)(n-2)(n-3), the n! implies you are decreasing
ex. IF n+1=5 then our n is 4 so (n+1=5) 4 (4-1=3) (4-2=2) (4-3=1) notice its 5,4,3,2,1 going down in value
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
i wonder why dont you use L.H rule there to solve the limit isn't it simpler or I am wrong i guess
Why ln y =1? If you differentiate the right hand side, shouldn't you also differentiate ln y too ? That is to say... 1/y = 1
where can i get the video on how to +1 for the factorial?
That's done to just cancel the n!. Remember n! = n x (n+1) x (n+2).....so (n+1)! = (n+1) x n!
how can we set the limit equal to y?????
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.
How could I solve the last example?
I am guessing divergence test
Sounds like a tire Mark Wahlberg which is great😂
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!
Are you from Boston?
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!!!
i did not understand why (-1)^n is not important sir. Can you explain more on that?
24:00 This is 4 months later, so you probably know this alr, so ig this for the future calculus
nerds.
the (-1)^n or (-1)^n+1 only alternates the series from positive to negative. (-1, +1, -1 etc. for (-1)^n) and (1, -1, +1 etc. for (-1)^n+1). But this is not matter when doing the ratio test because the absolute value is taken which makes (-1)^n and (-1)^n+1 always equal to positive 1. If you multiply something by 1 you get the same thing so it is irrelevant in this case. hope that helps gl u peopel. :)
@@sushi9521 thanks
12:58
Help I got confused at this part. Where did the "n !" appeared at the denominator, where did it come from? Pls I really need to know.
its by opening (n+1)! into (n+1)n!
its a basic concept. you can find it on google if you didnt get .
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.
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
Perfect presentation! what program is used for the presentation? Can we avail it?
11:07 if we don't simplify to this point, then the answer is 0. Because of 1/(infinity)2
1:14 the test is inconclusive, not the series.
This comment is irrelevant but I think I'm falling in love with your voice.😂
These become much easier if you just memorize that the limit as n goes to infinity of [ (n+1) / n ] ^ n = e
the last example is confusing because when you simplify at first you should have -1. therefore -1+1=0