What is a Series
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- Опубліковано 2 гру 2008
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !!
What is a Series - I try to give a basic idea of what a series is. I also briefly discuss geometric series and the test for divergence.
"Another one." - PatrickJMT, 1:32
330k people sat patiently and watched a 12 min video about series....this is heartwarming
Patrick, I will be telling my kids, my kids' kids, and my niece's and nephews about your heavenly videos. Your legacy will LIVE ON
2013 guy have u got kids now
How is life???
@teluguc uh, there are playlists for calc 1, calc 2, and calc 3 on my channel. not to mention that i also organized all the calculus videos on my website and put them in sequential order...
I am almost done with cacl 2, and i have to thank you. Yours videos helped me have an A so far.
Jesus Duarte Now time to take an english course c:
+Cheaper lmfaooo
Loool. Yes, he does not write properly. But he speaks two or more languages meaning that he has more resources than you. Now, it is time for you, Cheaper, to learn more languages.
back and forth Poet *hey dumbass,* it's quality over quantity. Doesn't matter how many languages you learn if you suck ass on all of them. It is better to know one language really well instead of half-assing two languages.
Skipped Calc 1, went straight into Calc 2 for Engineering this summer and I passed with a B+ thanks to Patrick!
wtf ur allowed to just skip cal 1? thats some bs
@@karl-anthonytowns856 ever heard of ap?
@@user-rf4vc7mt4d That's not exactly skipping the class, just taking the class in a high school environment.
@@user-rf4vc7mt4d Pretty sure everyone is thinking of college, not some BS high school class.
Wtf are you guys on
all this time finally realized Patrick is left handed
He's using the same trick as everyone who writes on glass, but sort of inverted. He's actually right handed but writes everything backwards.
@@veritasiumaequitasius3530 No point for such a trick when you write on papers.
Thank you Patrick :) I wouldn't have got a really good mark in Calculus 2 without your videos. Thanks again.
Excatly 10 years after releasing this video I am preparing myself to tomorrow series test. Thank you Patrick for all your job ;)
Thank you so much Patrick... I find Series quite hard to understand, and this video clarified so much for me.
@phoLegit this formula works only for geometric series where -1 < r < 1
"anotha one" - patrickJMT
I love the videos. Your practice problems are so useful! They are very relevant to my material and that's a big feat since I've witnessed many youtube channels fail in that regards (in math, physics, etc.). I even take notes along with you as if you were my professor AND I even credit your youtube channel at the top of my notes each time!
I really like how you write your summation sign, mine looks more curly. I'm totally stealing it. Also, I love your videos for review. I don't struggle in Calculus II but the few days before a test I watch all of the videos on the subject matter of the test just because it grinds it in deeper. Knowing what I'm doing makes me appreciate your videos more, also. I don't think a lot of people realize how much patience it takes to explain such in-depth concepts at such a simple level.
@ActorGuy yes, yes. everyone wants a playlist. they are just very very very tedious to maintain, but i will get around to it. i just hate tedious things so much.
very true: prime numbers play the key role in encrypting data
Thank u for explaining series in a simple and understandable manner :)
Why can't everyone make concepts this clear and concise? YOU ARE MY HERO.
Thank you for your videos, Patrick! You are very helpful! ^_^
@welk0metohell you can make a donation on my website if that feels less weird ; )
YOU HELPED MY NEPHEW A LOT THROUGH THIS VIDEO
if you sum a constant repeatedly, you will get either positive or negative infinity depending on the sign; hence it diverges.
Dude these videos are the best calc videos I've found!! (And I've gone through quite a few. heh.)
Thank you so much man from egypt :D
you saved my gpa
I'm from Algeria, and I find this very helpful , thank you Patrick :)
Wow. The thing you said after your examples was something I've been looking for for months. Just an explanation of it. I finally understand why it needs to be zero, fully. I just kind of knew it had to be 0 but not why.
Thanks so much for this video series on series! (teehee see what i did there?)
I was using khan academy for math, but after watching some of your videos on sequences and series, I'm a total convert. Your videos are amazing! Thanks so much. :)
-multiple engineering freshmen
Thank you for the video and explaining every topics clearly.. Your videos help me a lot.. :)
Thank you
You inspire me to do it
congrats, glad i could help you out a bit!
you are amazing! thanks so much! i was so confused with series
Thank you so much. You're the best!
Thanx a lot .. it's really very useful
Great video. Thanks a lot! Just wanted to say that in addition to the limit not equaling zero, if lim as n-> infinity does not exist, then the limit will diverge. (i.e. (-1)^(n-1) ).
Way to go Patrick! Thanks
only if both are positive : )
otherwise -3/1 would not work (negative 3 is less than one)
Always jamming with The JMT!
Ty From Peru nice Job .
use test for divergence
limit as n goes to infinity of arctan is pi/2, so the series diverges!!
Your mind is beautiful and your videos are super helpful!
Patrick....love your work. If I could make one suggestion it would be to maybe group these Sequences and Series videos in the typical order given in say either Stewart or Thomas. I'm in Calc II and I'm just sort of figuring out which to do first. But my prof has been mixing everything up for two terms now anyway. LOL.
Which text do you base your examples on? We are using Thomas 11th Edition.
awesome video
lmao good old fashioned patrikJMT definitely shot on a toaster but still a great video.
well, it was made over 10 years ago :)
thanks! this was very helpful!
just wondering dont the markers smell a lot?
awesome! thanks! i did not even know such a thing exists... ;)
You sir, are a saint!
You're my hero❤️😭🙏🏼
T is defined:
n+1
Sigma a^i
i=1
Sigma is the summation mark, symbol or whatever. n+1 means how many elements you have to count. Since you end at n you always have n+1 elements.
It's a sequence An = a^n and you have to find or express or define or whatever the word is, the sum of all the elements in that sequence.
Thank you very much!
thanks!
usually if there is a sequence of numbers you can find a general rule for working out the next number if you know the previous number. i tried to do this for prime numbers but it seems really hard.
@yadeniky that would make too much sense to do ....
Hi, Patrick,
This video was awesome,
Can you help me out with what sequence should I watch your videos, I want to learn sequences and series completely, I know the basic stuffs completely.
I would like to know different techniques to find if the series is convergent or divergent,
absolute and conditional convergence !
Leibnitz test for convergence of alternating series
Kindly help :)
Keep up the good work :)
patrickJMT Is the test for divergence is for Arithematic series or any series????, bcoz you explained only w.r.t 1st example(i.e., Ari thematic one).....???? Please help
You are a God at explaining! Why do we need books when we have you?
03:31 best tip in finding that sort of patteen?
you seriously are the BEST!
Mckenzie Mcmillian I love you
bruuh you are replying to a comment that is 4 years old, she is probable dead. let her rest in peace man.
@@dawood.jarral 😂😂😂😂
you just made me understand something i thought it was impossible for me to get it !!!!!!!! :-o
imagine learning this in Mandarin... well... i got your videos by my side.... thanks
Spending too much time on youtube slacking when I have math to do. This is my saviour T_T
I will make sure that my fathers, fathers, grandson learns from you :)
I needed it so much .. but this video is not working .. giving error :(
anyway thanx for all of your videos ! Great videoas and very helpful.
Even your comment replies are clear! You sir, are awesome.
I admire you
not sure what you mean...
I have my calc 2 final today, calling my inner Patrick to pull through the exam ,,,,,,,,,,,,,,,,,,,,
great video... i learned more in 12 minutes than i did in 4 college lectures haha
Hey patrick , firstly, thanks for saving the whole world:) Could you please tell me why this geometric series(10/9) is convergent even if its limit is not equal zero? Actually I don't get it. Please save me again
"...when they get small enough fast enough" - When is the small enough fast enough? Is there a certain rate of decrease where series would become convergent?
..well to answer myself, I guess that is determined by the common ratio...
@patrickJMT Understood...tedium is a pita for sure. Great stuff on the Calc 3 videos as well. Looks like Linear Algebra for me next term.
Could you give an example where the limit of the sequence is zero, but the series still converges? I can't seem to make sense of it in my head
Hello , could we use series in civil engineering surveying
Wait but I thought that 1+2+3+4+5+6+7+8...=-1/12 ?
@@Synthanicmusic 😂😂😂
thanks for everything bro. you rock. I'll donate more money to you!
Happy World Teachers' day Mr. Patrick! :]
@baglady999999999 only requirement: many thoughtful hours
@patrickJMT
Hahah, your remarks always make me laugh Pat. Mind if I call you Pat? I've been watching your vids for so long that It just feels that comfortable.
nice well done
ha, well, not that much there at the moment
Learn more on youtube than coming to class. Feels weird for paying tuition!
at the end, the "test for divergence" is also very often called the nth term test. because test for divergence is kinda vague.... correct me if im wrong?
Hi, Patrick. I just looked at my Calclus textbook by Larson, and I saw that if the absolute value of r is in between 0 and 1 (not -1 < x < 1), then the series diverges.
That's because absolute value can never be negative.
comon son...
THANKS A LOT
UTBMat 1120: Geometric Calculus II with UA-cam. That would be my dream class.
Glad to know sum-body still has a sense of humor.
No one can make me understand Summation Of Series.
PatrickJMT: Hold my sharpie!
;)
isnt there a formula for infinite series?
where it is a / (1-r)
where a is the first number and r is the common ratio
where ?
i'v tried to come up with the series for prime numbers but i'v had no luck so far. can u help me
I m not good with English terminology in maths. As i understand a series is the sum of a sequence? I remember in sequences you exlained it like a1, a2, a3 .., an. In series you explain it like a1+a2+a3+....+an.
I can't get how a series with the terms converging to zero can diverge, if the terms are nearing zero doesn't that mean that the sum is approaching a final value?
great!
i don't know why but seeing a lefty explaining math makes me able to understand math better..
at 7:39 you have "a/1-n" shouldn't it be "a/n-1" because when you plug in "n" values in "a/1-n" you would get negative numbers. Am I wrong?
PatrickJMT for president
Wait, why couldn't a series converge to a finite value? Why does that always mean it diverges?
WHY oh why do i only discover these videos a few hours before my exam. WHY NOT BEFOREEE!!!
Does the Test of Divergence apply to the Geometric Series? I'm just a little bit confused because the Geometric series goes to a number that is not zero (10/9) but it converges.
I don't get it too after 7 years
Patrick, i know this is probably a stupid question, but what is the summation of a constant? I mean, intuitively for me i'd say it converges, right? But by test for divergence the limit of a constant is a constant, and it doesn't equal 0, so it would mean it diverges. What's going on??? (if anyone can reply that'd be awesome, it's urgent)
Hey mate, time flies, I asked the same question 5 years later than you :) I dont get it too
Can you do a video with arithmatic or geomatric sequences when for example you know a14=56 a21=67 and you have to find the nth term or a1 or a65.
If a series has a limit doesn't that mean that it converges? And when the "limit" is infinity that means that it diverges?