Choosing Which Convergence Test to Apply to 8 Series
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- čas přidán 24. 02. 2019
- Deciding which convergence test to apply to a given series is often the hardest part of the unit on series convergence. In this video, I'm going to loosely walk through some larger strategies for picking and choosing the method, focusing on 8 different series and 8 different methods:
Geometric Series
Integral Test
Divergence Test
Alternating Series Test
Comparison Test
Limit Comparison Test
Ratio Test
Root Test
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this guys speaks so enthusiastically about this subject while I'm stressing about my exam lol
Haha, good luck!
@Oakley Christopher Go to hell scammer
@Draven Callan Go to hell bot #2
Same
i know Im randomly asking but does anyone know of a tool to log back into an instagram account?
I was stupid lost the password. I would appreciate any tricks you can give me
1 hour till my final for calc2 , guys this course is heavy af
Fadel Almobark 4 months later I’m here for the same reason. Due at midnight tonight lol
@Pete My final is in 2 days
1 year later, I’m here too
@@faya943 good luck
i am here before half an hour
I appreciate the enthusiasm. Helps when I'm watching this at midnight for some last-minute cramming. Very helpful, thank you!
GOod luck!
did you pass?
Dr. Bazett if you were my calc professor I'd have an A. You explained the ratio test as an extended version of the geometric test and concisely explained the difference when to use the direct vs limit comparison tests! Thank you for this!!!!
When your teacher explains 2 hours for one type of convergence test, this video explains 8 of them for only 12mins..... Thank you for uploading this video! Helped a lot !
Glad it helped!
This is one of the most concise and efficient review videos of series/sequences I've come across in my late-night-before-exam cram
this video is fireeeee my tests in 2 hours this is exactly what i needed
I want to be as excited about anything in my life as this guy is about convergence testing
This is seriously one of the best structured math videos Ive seen, so damn useful. Well done!
Exactly what I was looking for. Please make another video discussing more examples.
thank you!! it’s sooo hard to find concise videos like this
Thank you for this really nice video, Dr. Bazett!! Thank you for going to the details of why you did what you did instead of just presenting the solutions!
I had trouble with determining what to use, so thank you so much for making this video!
Thanks so much, Dr. Bazett! I can see the patterns to use to differentiate and evaluate these various series.
great great great! thank you so much also thank you for your elevated energy in this question, feels so much healthier and happier to be learnign from someone so excited to share this :)
I have a series test now and I didn’t understand how to differentiate them til now thank you
This guy speaks very passionitly and its amazing keep up the amazing vids homie!
Found this right before my final, you're a life saver!
Thank you, Dr. Bazett for creating helpful videos. The quality of your production is amazing. I wish to learn more from you. I hope to make videos similar to yours.
Good luck!
Thank you for this wonderful video which gives a summary of convergence test techniques. I also like the energy I feel when I watch your videos.
Great summary and quick practice problems for the methods!
Thanks from the bottom of my heart. You truly are a legend ❤️❤️❤️
EXACTLY WHAT I NEEDED !!
I wished he explained where he got that 1/25 from on that first geometric series. "I can pull out 2 factors of 5..." isn't quite clear. Just a random 2 factors?
When he goes over the solution to the geometric problem, notice how the 5 has a power of n +1 and not the n - 1 ? He means you need to “lower” that power to the n - 1 for it to nicely match the numerator. So what will bring the n + 1 to the n-1? Remove 5 twice. Aka you remove a 1/25 from the original problem.
you seem so proud of your progress and im over struggling and giving up
This was so helpful oh my gosh!! I was so stressed about choosing the right test to use during my exams and this really cleared things up!!
Good luck!!
Very clear and instructive. Thank you
Thanks for saving my math... this is really helpful!
Fast and clear. Good job!!
Really helpful, sir! Thank you! Have a test coming over this Wednesday, and I have a feeling that it will go well
Best of luck!
this video was a goldmine for me! Thanks a lot
I just wanted to know what different tests are there.
He just served my purpose 😍, without actually knowing it.
favourite math teacher, best graphics 👌
Thank you for uploading this video. Helped a lot.
We love you Dr. Bazett!
awesome, cool to have a refresher for all of the tests
great video, super helpful and much clearer than my professor
Correction: For the series on the bottom right at 0:25, I think you mean n=2 to infinity, not n=1 to infinity. n=1 entails dividing by 0.
Awesome experience of studying from your lectures✨.. really very helpful💫
I searched Many Many channels, Finally i got the greatest among all🙏🙏🙏🙏
great explanation, thank you!!
Haven't gone to any classes and now I'm cramming for the test today.
Well Im a lecturer at University of Karbala ( Iraq) and I sent this video to my student cause its simple method to realize which test of series you should choose . thanks to you
Doctor Bazett, this is a great video. Keep it up!
Truely amazing no words
Forgot all about these test. I remember I had fun with them in university :)
Your voice makes me feel like I can actually learn this course
literally a life saver
So helpful Thanks a lot!!!
Wow, awesome, just wanted this explanation 👏👏
Glad to hear that!
That was a great video. Love this
Hi, I have a question that for the divergence test, if we are calculating the sum k=1 to infinity of 1 over 2k+3, when I am doing with divergence test, its sequence goes to 0, thus it is converging, but when I am doing with the Comparison test, it is diverging. What's the problem?
I think in the divergence test example we can only conclude when the modulus series is convergent as when the modulus series is divergent then we cannot conclude that is because alternating series has alternating +, -. We have the case of conditionally convergent if sigma|un| is divergent and sigma un is convergent. So it is wrong to conclude if the modulus series is divergent
really helpful.Thank you
thank you, it really helps me prepare for my final exam !!
Best of luck!
Amazing content man. Very clear and helpful.
Good work dr!!
watching this before my calc 2 final, thanks for helping me cook
Thank you !! You're a saver
thank you sir so much you are the best of them allllll
Thanks my dude!
bro you made cal soooooooo easy and interesting for us..... thanks a lot.......
Just wondering, for 4:44 doesn't failing the alternating series test mean it doesn't approach 0 which means it is divergent?
For \Sigma sqrt(n^3+n)/(n^4-n^2) is the following a valid test for divergence / convergence: sqrt(n^3+n)/(n^4-n^2) < n^2/(n^4-n^2) < n^2/(n^2(n^2-1)) < 1/(n^2-1) < 1/n^2, and in the limit 1/n^2 tends to zero.
for the alternating series, how do I know if that is increasing or decreasing?
Great video sir. Keep it up
Sir, can u please tell whether the series an = (-1)^n+1/((n+1)^1/2 +( -1)^n+1) is absolute convergent and which test can be used in this?
Watching 1 day before exams thanks..
10:43 The limit as n approaches infinity of 1/sqrt(n) diverges not coverges. The series is a p-series with p = 1/2... a p series is divergent for all p < 1.
Fabulous work dear
I am here enjoying your communication skills 🥰
Great video!
in that example of Alternating Test Series, isn't it supposed to be '-1/rootn < 0'. ?
1) Divergence test:
lim a(n) =/= 0 ==> series diverges
2) Comparison test (to p-series/geometric series):
a(n) a(n) converges
3) Limit comparison test:
lim (a(n) / b(n)) = c > 0
b(n) converges ==> a(n) converges
4) p-series & geometric series:
4a) p-series:
Σ(1/n)^p converges p > 1
4b) Geometric series:
Σa*q^(n-1) =
{ a/(1-q) if |q| < 1
{ diverges if |q| >=1
5) Integral test:
Integral from 0 to oo f(x)dx converges ==> Σf(n) converges
6) Alternating series test:
Σ(-1)^(n-1) * b(n)
if b(n) > 0, decreasing, lim b(n) = 0
then series converges
7) Root test:
lim root(n, a(n)) = L (if L is finite, series converges)
8) Ratio test (d'Alembert) (good for factorials & exponents):
lim a(n+1)/a(n) = L
if L < 1 ==> series converges absolutely
if L > 1 ==> series diverges
if L = 1 or doesn't exist, use other test
It's It's shame I only found you the day before my Calc 2 exam. Oh well, better late than never.
helped me a lot
Really good video i loved it
for Σ(-1)ⁿ ln(n), can you just look at it as
Σ|ln(n)|
and by divergence series test it diverges?
8:42
If the sequence was powered by n^2, what should we do?
Hey doc very nice presentation .Keep it up..From the philippines
10:21 ne^(-n^2), Would using root test faster? I really hate using integral test.
This video saved my life
very useful!
got my ap exam today thank you🙏🏽
How the heck do you get 1/25 for the second one?
Plug in 1 for n and you get 1/25
wow this was super helpful
Si plz tell me from which book do u pick up these problems???
Thanks!
Hey sir I have no clue hw you got the answer for the limit comparison one, any chance you could help me out? final is tomorrow
You're so good ❤️
Very much useful vedio
I love you and I love this video - thank you
Does anyone know what song is played during the last part
Never have I seen a man so excited about alternating series.
I am here with 30 min left for my exam and binge watching anything that can serve as a shortcut 😭😭. Wish me luck
Are there more videos like this?
So. Freaking. Helpful!
amazing video
Brilliant
Well Done 😎