Dude...I have an associates in science and am currently double majoring in petroleum engineering and biochemistry with a chemistry minor. With that being said, I would like to thank you for helping me achieved what I have during my studies thus far. I've watched your videos for a long time now and have never shown my appreciation. You are a fucking awesome person!
It's weird this math existed in 2008. Obviously it's not werid. But. I was so young at the time, it's like this math was lurking in the shadows waiting for me to go to college then attack me. But your videos are very helpful and serve as a good defence against this monster.
You are my Math God! I can not describe how I feeling, I'm a student of METU, in first exam I got 41. and then 1 day before my second midterm, I found your channel I watched videos as much as I can and I got 71-curve of the exam is 46- thanks a lot thanks a lot.. much love from Turkey Pat:))
Thanks so much for your patience in explaining the approximation of the sum of the alternating series so clearly. I have been puzzled with the way my textbook explains it for such a long time. I am so grateful for your help!
I just found your videos, Great work man! I'm studying for my calc 2 test tomorrow and the only thing I didn't understand was this estimation theorem. (missed that class) Now I get it and I'm confident for my test. Thanks!
Thank you so much! I'm currently taking Calculus. My teacher is nice but her teaching style is not simple as yours. She teaches to get the lesson done so she can get her paycheck, not because she wants use to truly learn math. I visited your website and it helps A LOT. You made it so much easier. Thank you.
ahhh ok, it is conditionally convergent : ) in many books, when one first learns about alternating series, you do not yet know about absolute/conditional convergence, so i figure it would just confuse people to throw that terminology in there at that point
so clear and straightforward! your videos play right into my learning style of annotated exercises and i can replay this at my own pace! unlike in the lectures
Thanks for the good review. We have an exam tomorrow in Calc 2 on infinite series. I've been trying to find information on how to determine whether the error for an alternating series estimation is an overestimate or an underestimate...
How do you it? You make it so much clearer and easier than James Stewart and my calc professor. Real talk - you should be sainted. "Saint Patrick JMT." Saint of mathematics.
whats up Patrick, Im stuck on a series problem and would like to know what video you can direct me to not to solve this particular problem but just to understand the concept and approach. The problem is: SUM for n=1, to infinity of 4/(4n-3)(4n+1)
This method and explanation has helped me a lot as with all of your other videos. But when I tried this method with arctan(0.5) to 3 decimal places it tells me that rejecting the 5th term will give me the desired accuracy but that gives me 0.463 and the correct answer is 0.464. I was wondering if I could get some help with this as I have a final coming up really soon. Thanks.
Thank you this is really helpful. But what of when N is really big is their a way to sum up Sn without doing the addition by hand? and here is the specific problem I'm working on ∑n=1∞(−1)n+1(n+2)(n+10) with an error of at most 10^-3.
Hi Patrick. If you don't mind could you help me please? So I have to find 3 diffrent values of u ( (-1) ^n * (1/(1-u))* 4n ) / (2n)! = -1/2 I tried to do with estimation...but I have no idea... then I tried to do limit comparaison, but it does not tell me the sum of the series. or should I use Taylor theoreme? Please I am literally begging you how to solve this. Thank you
actually i noticed something with the second example here, apologies if this was already mentioned or if it's an invalid argument but the 6th term would add 0.000023... to 0.098785... that makes the new number 0.098808, with the next number substracting some part(probably smaller than 0.00001), so the 4th decimal is actually incorrect
I was a little pissed to hear that you wouldn’t offer a rigorous algebraic explanation of how to solve the inequality error_n < T, where T is a given threshold. But after working a bit on my own I have realized that it’s kind of brutal to get to that kind of surefire method, this outweighing the simplicity of brute-forcing it. However, for crazy thresholds or whatever one would like to call it, I think it’s probably best to work the inequality algebraically until there’s something simpler to brute-force
@patrickJMT I was expecting either an alternate estimate or an integral estimate to show up on my exam (that I took between my last comment and this one) but it didn't anyway
Dude, I’m pretty sure you’re still active, so hopefully you’ll update this with an algebraic example. This brute force method isn’t that helpful when the bound is something weird like 7/5^7 or sqrt(pi)
Dude...I have an associates in science and am currently double majoring in petroleum engineering and biochemistry with a chemistry minor. With that being said, I would like to thank you for helping me achieved what I have during my studies thus far. I've watched your videos for a long time now and have never shown my appreciation. You are a fucking awesome person!
It's weird this math existed in 2008. Obviously it's not werid. But. I was so young at the time, it's like this math was lurking in the shadows waiting for me to go to college then attack me. But your videos are very helpful and serve as a good defence against this monster.
You are my Math God! I can not describe how I feeling, I'm a student of METU, in first exam I got 41. and then 1 day before my second midterm, I found your channel I watched videos as much as I can and I got 71-curve of the exam is 46- thanks a lot thanks a lot.. much love from Turkey Pat:))
😠
Thanks so much for your patience in explaining the approximation of the sum of the alternating series so clearly. I have been puzzled with the way my textbook explains it for such a long time. I am so grateful for your help!
glad you like my videos :) come back often!
I just found your videos, Great work man!
I'm studying for my calc 2 test tomorrow and the only thing I didn't understand was this estimation theorem. (missed that class)
Now I get it and I'm confident for my test. Thanks!
I have a test in an hour and didn't understand this stuff. Now I do. Thanks so much, you're my pre-test ritual.
Thank you so much! I'm currently taking Calculus. My teacher is nice but her teaching style is not simple as yours. She teaches to get the lesson done so she can get her paycheck, not because she wants use to truly learn math. I visited your website and it helps A LOT. You made it so much easier. Thank you.
@fhunkymonkey no, taylor's theorem does not work that way; it is a bit more complicated
also your examples are perfect. concise, yet covering a broad range of ideas. really stellar stuff Pat keep it up. many thanks
You've won the day bro. I've looked upto khan academy and The Organic Chemistry Tutor , but nobody made any sense instead you did. Thanks.
This was soooo helpful! I was stuck on a problem like this for a half hour and you saved me in 30 seconds!!
@iammaxhailme well, this only works for alternating estimation theorem
ahhh ok, it is conditionally convergent : )
in many books, when one first learns about alternating series, you do not yet know about absolute/conditional convergence, so i figure it would just confuse people to throw that terminology in there at that point
best explanation of this theorem on TH-cam - thank you man
so clear and straightforward! your videos play right into my learning style of annotated exercises and i can replay this at my own pace! unlike in the lectures
Thanks for the good review. We have an exam tomorrow in Calc 2 on infinite series. I've been trying to find information on how to determine whether the error for an alternating series estimation is an overestimate or an underestimate...
your videos are so good. Short and direct to the point
ha! god of math! not quite, but i appreciate the nice words all the same! good luck on your midterm!!
@FaiththeHairstylist yep, and it makes total sense!
You teach incredibly better than my math professors. Thank you so much for the videos!
how can I do exercises like this without a calculator!!? because it isn't allowed in exam
you add fractions manually
you must be a student in CSU ha!
Well I'm assuming you already took the exam, but they likely would not put anything too crazy on an exam that wouldn't require a calculator
Calc 2 at UVA is also done without a calculator but the professors know and go easy on the calculations.
Watching your videos is WAYYYYYY more productive than listening to my prof - Thank you, your website is amazing! XD
really helpful man! I missed this lecture in class and would have been completely lost without this vid
thanks to your videos I probably got an A on my last exam
You deserve my tuition
The best teacher created the best videos!
How do you it? You make it so much clearer and easier than James Stewart and my calc professor. Real talk - you should be sainted. "Saint Patrick JMT." Saint of mathematics.
your videos are now an essential part of my studying. Thank you very much!
This is 12 years ago and still so useful
this is extremely clear you must be a great math tutor!
@geebauer just doin' what i can
Is it correct to assume that this will work for an alternating power series as well, given a situation where we know what n and x equal?
Why is it four zeros for four decimal places? Would it be three zeroes instead since it's accurate to the 4th decimal places?
Thank you, your instructions are clear and coherent! It makes perfect sense, and I definitely understood this at an applicable level!
Be my teacher!
hey! a 'B' is good! nice job! : )
whats up Patrick,
Im stuck on a series problem and would like to know what video you can direct me to not to solve this particular problem but just to understand the concept and approach.
The problem is:
SUM for n=1, to infinity of 4/(4n-3)(4n+1)
This method and explanation has helped me a lot as with all of your other videos. But when I tried this method with arctan(0.5) to 3 decimal places it tells me that rejecting the 5th term will give me the desired accuracy but that gives me 0.463 and the correct answer is 0.464. I was wondering if I could get some help with this as I have a final coming up really soon. Thanks.
Thank you this is really helpful. But what of when N is really big is their a way to sum up Sn without doing the addition by hand? and here is the specific problem I'm working on ∑n=1∞(−1)n+1(n+2)(n+10) with an error of at most 10^-3.
Hi Patrick. If I want to solve it algebraically, and within 0.001, do I set a of n equal to 0.001? Thanks
thanks and thanks!
you going to study math in college?
Really helpful stuff even when I am solving the reverse sort of problem (given an error, but need to find interval of x).
Hi Patrick. If you don't mind could you help me please?
So I have to find 3 diffrent values of u
( (-1) ^n * (1/(1-u))* 4n ) / (2n)! = -1/2
I tried to do with estimation...but I have no idea...
then I tried to do limit comparaison, but it does not tell me the sum of the series.
or should I use Taylor theoreme?
Please I am literally begging you how to solve this.
Thank you
waited 6 mins of my life (because that's when I noped out). You're explaining this concept in a very snake-oil selling way
i have no idea what you are trying to say
actually i noticed something with the second example here, apologies if this was already mentioned or if it's an invalid argument
but the 6th term would add 0.000023... to 0.098785...
that makes the new number 0.098808, with the next number substracting some part(probably smaller than 0.00001), so the 4th decimal is actually incorrect
the best teacher ever!Thank you!!!
Some teachers need to see your videos before going to class.
"Otherwise, it doesn't make any sense that you are talking it". love that line haha
thanks for your help!! I just got a 98% on my last calc II exam
98?? that's good. i have a calc II midterm tomorrow..taylor/mclaurin/series tests/vectors
im sorry congratulations
although it is a brute force technique, your way makes more sense than the way we went over in class.
near perfect sounds quite alright to me : )
were you doing those 8-powers in your head or calculator?
learned this in 10 minutes what wud actualy take 1 hour if i tried learning from the book.
thanks!
how do find b(n) :( im confused. i get the rest of the video but i just don't get it that one part.
Thank you so much for explaining this Pat. You're great!
how would you do this if you weren't allowed a calculator on a final exam...
You would probably not be asked something like this without a calculator. If you are, just leave it as fractions to show you know HOW to do it.
Isn't 1/n the divergent harmonic series?
@cacaloveforever i have gone back to the sharpie and paper
YOU ARE BAE. Thank you so much!!
mates a genius
Great explanation! Thank you
I was a little pissed to hear that you wouldn’t offer a rigorous algebraic explanation of how to solve the inequality error_n < T, where T is a given threshold. But after working a bit on my own I have realized that it’s kind of brutal to get to that kind of surefire method, this outweighing the simplicity of brute-forcing it. However, for crazy thresholds or whatever one would like to call it, I think it’s probably best to work the inequality algebraically until there’s something simpler to brute-force
Wait... how do you know which term is the first neglected term?
Thank you so much for your videos. Great for quick review!
What would the inequalities look like?
Is it possible to solve these algebraically?
thanks PatrickJMT
great videos man, helps a ton!
thanks a lot this method is quick and easy
Could you solve this algebraicly aswel as we are not allowed a calculator on our exams? Thanks :)
@patrickJMT
I was expecting either an alternate estimate or an integral estimate to show up on my exam (that I took between my last comment and this one) but it didn't anyway
1/n is a divergent harmonic series but (-1)^n 1/n is not, using the alterning series test
oMG that is so easy. I almost shut you off when i saw that first 15 seconds of mumbojumbo. e tu patric e tu? That should come after the easy train
In the first example, he added a +1 to the ^n, making his signs right. (at 2:05)
Never mind i got it T_T i just had one of those moments... BUT awesome vid. real life and time saver...
Thanks so much! It was really helpful.
thanks! :)
Thank you, Sir!
thank you so much you helped me a lot
Thank you... i wish you were my teacher
u are the BEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Aren't you should add the term with four zeros as well?
Great video!!! Thank you
@ShivMan007 ha, thanks : )
god bless you patrick
Youre a boss Pat
If you go to 1:33 in the video, he shows that the (-1)^n is what makes it an alternating series and the other part is your b(n)
i click on most of yer vids to add up to the views. my way of saying thanks. :))
Pat... You are my Homie.
Thank you
Dude, I’m pretty sure you’re still active, so hopefully you’ll update this with an algebraic example. This brute force method isn’t that helpful when the bound is something weird like 7/5^7 or sqrt(pi)
thanks! it is clear now
thank you so much
Thank you so much!!!
well done!
did i say something different - i do not want to watch it all and find it out
ha! thanks : )
Tyvm
you are amazing
Why does this have any dislikes
lim n->inf i/n = 0 because 1/n becomes so small and approaches zero