wonderful! glad the videos help. and nothing makes me feel better than to know that i am helping out another math teacher! good luck!! teaching is the most noble profession! : )
Just wanted to let you know that you have helped me understand in 10 minutes what my professor couldn't teach me in a week. And Patrick, you have no idea how popular you are. I'm in engineering and all of my classmates use your videos to get them through courses.
Your making a public service here, you should be rewarded. This is a public service that helps students from all over the world to achieve success. Greetings from Portugal.
I stopped the video half way because I almost broke down in tears. I'm actually understanding this thanks to you. There aren't any words to describe my gratitude.
Dude, this is awesome. My Math professor just lectured on this. My math professor is great but she skips over some things and makes you go in for office hours. Here, I can get all the important math details and you explain why it matters. Thanks so much for your videos. I've been using them to study for my mid-term I just took on Monday.
Yo Patrick! My name is Forrest Kingsley and I'm a mathematics instructor. You do a really good job, I love your videos. When I was still a student I used to watch your videos and they helped me a lot!
I find your videos very relaxing =) (not to mention enlightening!) Also, as a trainee maths teacher here in Australia, very useful as a nice style of teaching. Thanks heaps!
No kidding, this guy should be getting paid! My school, the University of Texas at Austin, uses his videos for a "flipped" class version of Calculus. This guy is pretty much teaching us, while our teacher just makes us talk to each other in class.
You are welcome, Patrick. If I may say, your videos are better than those by the Khan academy. Keep up the good work! I currently teach only basic level math but one day when I'm teaching calculus I will tell my students about your videos. You'll get plenty of views and likes.
well, sometimes you can use both. you just have to be able to justify the inequality in the direct comparison test. in general, if i think a problem can be done both ways, i usually opt for the limit comparison test (but i am also very comfortable at finding limits, which is something that gives some people problems!)
try it out and see if it works! i would have to rewatch the video and look at the problem. there are no hard and fast rules about what to compare a particular series with
hey patrick! thank you for your vids...i don't know what i would do without them. but i have one question..could you always use dct or lct? or does it matter depending the problem?
im getting ready to finish up integral calculus and will be taking vector calculus, linear algebra, and differential equations within the next year. PLEEEEASE tell me you will have videos for all classes by then if you dont already! i depend on your videos soo much! and im sure i am not the only one :)
Patrick, Thanks for your videos on Calculus. I am taking Calc 2 right now in the spring (7 weeks - Not the best idea). Your videos helped out a lot trying to understand the different tests. One of the issues I have is testing for absolute convergence for trig. I have looked at your other videos. An example I came across is the summation of cos ((kπ)/k) going from k=1 to infinity. This I realize is an alternating series. What would you do to test for convergence? Carbon Fiber X
awesome videos, super helpful!!! ive got a question though, is there any easy way to tell which test you use when you come up on a series? ive got a midterm on friday, and im pretty sure my teacher is just going to put tons of series on it. i can sometimes tell which test to use, but othertimes its harder...any suggestions?
When you solved the limit for the limit comparison test, the value '2' that you received does not represent the value that the sum converges to, correct?? It just gives indication as to which of the 3 rules of the limit comparison test to use??
Howdaycara Patrick, I thought I'd tell you that I succeed in teaching one of my pre-algebra students the power rule for differentiation!!! We are the cool smart guys you and I and together we will change the world! America has so much hidden potential, we will one day be smarter than Japan and China and Korea and India, together we will make it possible!
not really.... although my preference is to use the limit comparison, then direct, then integral test; i think LC is easier to use than DC which is easier than IT
When you're comparing, do you compare using interval [1, inf), or is it for all n's. If you have to use the interval, why can't you say that 1/n^3 is less than or equal to 1/n , which is divergent?
it needs to be similar to the original function. The only reason you are comparing it to something is because you can essentially omit the rest of the equation and only focus on what will have the biggest impact on the series as n increases infinitely.
Hi patrick i really appreciate and enjoy your tutorials . however can you give up paper and get a digital pen pad , too much of paper is wasted . just a suggestion.
I did the ratio test on the absolute value of cos((kπ)/2) and I found that it Diverges. I then tested it for Conditional Convergence and found that if you take the limit of cos((kπ)/2) you get either 1 over infinity or -1 over infinity which both are equal to one. I then looked at whether it decreases or not. I rewrote the equation as (-1)^(k + 1) times (1/k). I found the numerator of cos kπ just determines whether the sum is positive or negative. I then did the integral test.
Hey Patrick, your videos are a lifesaver. I do have one question though, after you tried to use 1/n^3 as a direct comparison and it didn't work after you changed the sequence to 1/n^3-4, why couldn't you just change your b sub n to 1/n^2 or something that we also know converges by the p test?
hey patrick.. I dont understand.. why do we ever have to use a limit test.. i know how you said that to use the direct comparison test you need to see if a_n is smaller or bigger than b_n. but does that really matter because if b_n converges a_n has to converge and if it diverges a_n should also diverge, right? because by doing the limit test we will end up finding if both of them diverge or converge..so my question is do we really have to use the limit test?
Patrick, this doesn't complement what you said about the Test for divergence, for the second example you said the limit = 2, and it converges. But the Test for Divergence states that if the limit is not = 0 then it diverges, our limit was not = 0 so how come it converges?
does this mean that the limit comparison test works for every problem that the direct comparison test?,so like it would be better to not even try direct comparison when u can have lim comparison test? loved your videos by the way :]
the limit comparison test seems pretty user friendly... one question though, is it safe to say that someone can use the limit comparison test wherever the problem does not call for the root test or the ratio test?
Hey there, I have a question about using the direct comparison test for infinite series. for using the direct comparison test, is it necessary to find out a comparison that's larger/equal to the original statement? Or we can do the same stuff for the comparison that is smaller/equal to the origin?
wonderful! glad the videos help.
and nothing makes me feel better than to know that i am helping out another math teacher!
good luck!! teaching is the most noble profession! : )
you are the reason i am passing calc 2
Saaaame broooo
Just wanted to let you know that you have helped me understand in 10 minutes what my professor couldn't teach me in a week. And Patrick, you have no idea how popular you are. I'm in engineering and all of my classmates use your videos to get them through courses.
God is going to reward you for this, you have saved me
I have a test on Tuesday and I'm going to binge watch your videos until then. (you got me an A in calc1 last semester)
Your making a public service here, you should be rewarded. This is a public service that helps students from all over the world to achieve success. Greetings from Portugal.
I stopped the video half way because I almost broke down in tears. I'm actually understanding this thanks to you. There aren't any words to describe my gratitude.
Amazing! This sunday i'll have calculus 2 midterm and these videos made me ready for the exam. Thanks!
I just learned 3 weeks of my Calc 151 class in about 30 minutes thanks to your videos! You are a great teacher and very helpful. Thank you!
Dude, this is awesome. My Math professor just lectured on this. My math professor is great but she skips over some things and makes you go in for office hours. Here, I can get all the important math details and you explain why it matters. Thanks so much for your videos. I've been using them to study for my mid-term I just took on Monday.
Yo Patrick! My name is Forrest Kingsley and I'm a mathematics instructor. You do a really good job, I love your videos. When I was still a student I used to watch your videos and they helped me a lot!
I find your videos very relaxing =) (not to mention enlightening!) Also, as a trainee maths teacher here in Australia, very useful as a nice style of teaching. Thanks heaps!
I haven't watched your other videos but you have the best series/sequence videos on youtube. Thanks so much for the hard work.
Thank you! Your videos have been helping me since high school! I always recommend your videos to everyone who's having problems with calc.
im going to pass calculus 2 with an A, you help me filling some holes. thank you!! :D
Filling holes 😂😂😂
I like you theone
what kind of holes are we talking about here
No kidding, this guy should be getting paid! My school, the University of Texas at Austin, uses his videos for a "flipped" class version of Calculus. This guy is pretty much teaching us, while our teacher just makes us talk to each other in class.
So huge shoutout to this guy. I got an exam on all series tests tomorrow and was dreading it until I saw these videos! THANK YOU SO MUCH
good luck!
if someone binge-watched all of these videos the day before their exam, i actually think they could pull a decent grade
lol naw humans cant retain that much information at once that well
That’s what I’m doing right now 😂
Scarlett Van Marie I just think it doesn’t matter if it’s taught over 4 months or in one night. It’s just hard to retain all of calc 2’s information
How about the day of the exam 😎
How about 30 minutes before the exam :)
thank you very much patrick , you truly have helped me in my calc 2 class. i dont know what id do without you.
your videos always calm me down from panic. you really are the greatest math teacher 😭💗
You definitely do. You saved me last year and are doing it again this year in my second year in Engineering
I just noticed you also posted linear algebra videos! That is so great. That's it, I'm subscribing!! :)
dude, has anyone ever told you that you are friggin' awesome for doing this on youtube? thanks
I don't understand how ANYONE can dislike this video...PatrickJMT Is frekin amazing
You are welcome, Patrick. If I may say, your videos are better than those by the Khan academy. Keep up the good work! I currently teach only basic level math but one day when I'm teaching calculus I will tell my students about your videos. You'll get plenty of views and likes.
i have my math final in a few hours along with my chem final. you saved my life, thank you
Before these videos, I was clueless. Now hours before my midterm, I know more than from going to my 9 am lectures.
Thank you, Sharpie ninja.
2 more weeks of caluculus left for me! Patrick you made me survive this!! thanks.
thanks for the vids...i have a test on Sequences and Series tomm in Cal 2 and ur videos really help!! keep up the good work
Just learned this today and ONCE AGAIN, you saved my life!
well, sometimes you can use both. you just have to be able to justify the inequality in the direct comparison test.
in general, if i think a problem can be done both ways, i usually opt for the limit comparison test (but i am also very comfortable at finding limits, which is something that gives some people problems!)
@anjicedtea you are welcome! i think there are a few videos left out of that playlist though!
try it out and see if it works! i would have to rewatch the video and look at the problem.
there are no hard and fast rules about what to compare a particular series with
years and years later, can't thank you enough
hey patrick! thank you for your vids...i don't know what i would do without them.
but i have one question..could you always use dct or lct? or does it matter depending the problem?
You are good my brother. You are very helpful. Thank you very much.
@purohiti yes, it for sure matters on the problem. sometimes, u can use both, sometimes only one seems to be applicable.
thank you so much! your videos are really helping me pass my calculus II class :)
thank you your videos are so straight to the point and easy to understand!
You're awesome! Understanding sequences and series just in time for my exam today :)
you are the best
I really understand that lesson after alot of searches
patrick, you're my new hero.
yes, u could use the same idea to justify that the value of one integral is larger/smaller than another
im getting ready to finish up integral calculus and will be taking vector calculus, linear algebra, and differential equations within the next year. PLEEEEASE tell me you will have videos for all classes by then if you dont already! i depend on your videos soo much! and im sure i am not the only one :)
@abthurd it depends on the problem
these videos saved me so much time! i get it now. you rule.
no prob
you've saved my life on multiple occasions. THANK YOU!
Thank you so much... its amazing how clear you make this stuff for me.
thanks for the kind words Mr. Kingsley!
Im watching ur video the night before exam and i think its really helpful
You are so much better than my Calc professor!!!!!
In your playlist, you have the order of your DCT/LCT videos mixed up. This one should come first.
Appreciate the help!
you are so awesome Patrick!
Patrick, Thanks for your videos on Calculus. I am taking Calc 2 right now in the spring (7 weeks - Not the best idea). Your videos helped out a lot trying to understand the different tests. One of the issues I have is testing for absolute convergence for trig. I have looked at your other videos. An example I came across is the summation of cos ((kπ)/k) going from k=1 to infinity. This I realize is an alternating series. What would you do to test for convergence?
Carbon Fiber X
ohhh thank you so much, you are so good at explaining things!
This is one of the hardest part in all calculus areas.
Angel Escobedo You don't need to be so mean like that. That was absolutely unnecessary.
What
The
When the powers are the same at 5:24, don't you still have to account for the 4? So it'd be -2?
no since n is getting really really big, the -4 in the denominator will not have a large impact since the degrees on the top and bottom are the same
no problem!
Agreed. I was lost when you started with the other vid. Thanks
thanks!
@ferasteddy this is not the test for divergence that i am using.
you can compare it to anything you wish! so long as you know it converges/diverges, and you get a 'useful' value from the limit
I LOVE YOU!!!!!! I wish you were my calculus teacher
is there a video on solving improper integrals using the comparison test?
how do you know when to do the direct comparison test and when to do do the limit comparison test?
Best teacher ever :)
@FaiththeHairstylist typically it seems like most of the time it has something to do with a p-series!
Thanks! You are my God of clarification!
awesome videos, super helpful!!!
ive got a question though, is there any easy way to tell which test you use when you come up on a series?
ive got a midterm on friday, and im pretty sure my teacher is just going to put tons of series on it. i can sometimes tell which test to use, but othertimes its harder...any suggestions?
When you solved the limit for the limit comparison test, the value '2' that you received does not represent the value that the sum converges to, correct?? It just gives indication as to which of the 3 rules of the limit comparison test to use??
Oh it's no doubt. TheIntegralCalc is a good channel as well, but your videos are exceptionally clear. Thanks for the great instruction.
Howdaycara Patrick, I thought I'd tell you that I succeed in teaching one of my pre-algebra students the power rule for differentiation!!!
We are the cool smart guys you and I and together we will change the world! America has so much hidden potential, we will one day be smarter than Japan and China and Korea and India, together we will make it possible!
Thank you for giving peace about what to do when the bn is smaller :)
thank you, you're the reason i have a chance to pass calc 2.
Thanks a lot Mr. PatrickJMT! :)
Why do you pull out the two in the first problem but not the second. Doesn't thay affect the answer
not really.... although my preference is to use the limit comparison, then direct, then integral test; i think LC is easier to use than DC which is easier than IT
When you're comparing, do you compare using interval [1, inf), or is it for all n's. If you have to use the interval, why can't you say that 1/n^3 is less than or equal to 1/n , which is divergent?
i typed in "comparison theorem" and "comparison theorem patrickjmt" was the first suggestion
^_^
it needs to be similar to the original function. The only reason you are comparing it to something is because you can essentially omit the rest of the equation and only focus on what will have the biggest impact on the series as n increases infinitely.
Hi patrick i really appreciate and enjoy your tutorials . however can you give up paper and get a digital pen pad , too much of paper is wasted . just a suggestion.
I did the ratio test on the absolute value of cos((kπ)/2) and I found that it Diverges. I then tested it for Conditional Convergence and found that if you take the limit of cos((kπ)/2) you get either 1 over infinity or -1 over infinity which both are equal to one. I then looked at whether it decreases or not. I rewrote the equation as (-1)^(k + 1) times (1/k). I found the numerator of cos kπ just determines whether the sum is positive or negative. I then did the integral test.
Hey Patrick, your videos are a lifesaver. I do have one question though, after you tried to use 1/n^3 as a direct comparison and it didn't work after you changed the sequence to 1/n^3-4, why couldn't you just change your b sub n to 1/n^2 or something that we also know converges by the p test?
If the series was ln n/n^3, would you still compare it to 1/n^3?
thank you for making these videos!!
hey patrick.. I dont understand.. why do we ever have to use a limit test.. i know how you said that to use the direct comparison test you need to see if a_n is smaller or bigger than b_n. but does that really matter because if b_n converges a_n has to converge and if it diverges a_n should also diverge, right? because by doing the limit test we will end up finding if both of them diverge or converge..so my question is do we really have to use the limit test?
By finite positive, can a(n) / b(n) be equal to 0 for the test to work?
Patrick, this doesn't complement what you said about the Test for divergence, for the second example you said the limit = 2, and it converges. But the Test for Divergence states that if the limit is not = 0 then it diverges, our limit was not = 0 so how come it converges?
Dude you totally burped in the first 10 second of this video! thanks for the laugh.
does this mean that the limit comparison test works for every problem that the direct comparison test?,so like it would be better to not even try direct comparison when u can have lim comparison test? loved your videos by the way :]
Fantastic work
the limit comparison test seems pretty user friendly... one question though, is it safe to say that someone can use the limit comparison test wherever the problem does not call for the root test or the ratio test?
I LOVE YOU THANK YOU SO MUCH. Missed this lecture in class and you just saved my ass, thanks again!
@SpnFan04 that is a good question
okay, I'm just confused.
When can I use either the direct comparison test or the limit comparison test?
Hey there, I have a question about using the direct comparison test for infinite series.
for using the direct comparison test, is it necessary to find out a comparison that's larger/equal to the original statement? Or we can do the same stuff for the comparison that is smaller/equal to the origin?
This was so helpful! Thank you!
Wow Thank you very much.... You are great... God Bless you ...
Flying colours from now on
i had the same question as Attackgoat2, why do you have to compare it to something similar? or do you have to?