This is where Calculus II slowly comes to an end. This Power Series Practice sums up all the fine methods we learned in Calculus from day one. Professor Breiner thank you for another superb lecture.
Simply wonderful! It took me months to understand Power series, If only I had Christine as my teacher. Crikey my daughters are going to be surpassing their old man before they're teenagers by being able to watch this stuff. Thanks
WOW, thank you Christine, those videos are really helpful, As an Engineer I start to like Math again and by beeing able to do those problems I feel so confident to even help others :-)
In d), again, the first term is always a, =1 here. Then the subsequent term is always x times the previous, a geometric sequence whose series converges to 1/1-x, /x/
In the example (d) you made the index substitution m=0, then m = n +1 which leads to the known solution for the Geometric Series 1/(1-x), It was nice. But, following the logic and method you used in example (b), we can factor the series (d) into sum (x * x^n) which becomes x * sum ( x^n ). Then the first term of the series we have now, which starts at -1, is 1/x followed by the Geometric Series. So, we get here x * ( 1/x + Geometric Series) = 1 + 1/(1 - x). This result is different, and better.
very intuitive, d was a little tricky. If teachers were selected based on their ability to teach efficiently then there would be more lectures like this!
why e^x, is that belong to the integral form of x^n/x!? since the denominator is factorial so the derivative of e^x doesnt belong to this (the n can't be canceled out comparing to n with n! (factorial))
Dear Christine, you have made a slight mistake regarding the infinite sum of your GEOMETRIC series (GS) in parts (b) & (c) etc. So let me try to correct it: GS is converges APPROXIMATELY to (1/1 - x), if and only if , the value of x is strictly POSITIVE and less than 1 (i.e. inside/within the OPEN interval (0,1)) . Do check it !! KUDOS
![Noob To Max With DRAGON REWORK In Blox Fruits [FULL MOVIE]](http://i.ytimg.com/vi/LnBMOinoOvA/mqdefault.jpg)
Omg how patient she is... Best teacher I have ever seen
This is where Calculus II slowly comes to an end. This Power Series Practice sums up all the fine methods we learned in Calculus from day one. Professor Breiner thank you for another superb lecture.
Simply wonderful! It took me months to understand Power series, If only I had Christine as my teacher. Crikey my daughters are going to be surpassing their old man before they're teenagers by being able to watch this stuff.
Thanks
I just love how she makes it look so simple!
WOW, thank you Christine, those videos are really helpful, As an Engineer I start to like Math again and by beeing able to do those problems I feel so confident to even help others :-)
superb lecturer, even dummies like me can understand. Thank you Ms Breiner and please keep instructing.
You are an excellent teacher. MIT is lucky to have you.
Best teacher ever! I want to buy her a drink.
i love you so much. you're an amazing teacher.
A wonderful teacher!!!
wow so many of my questions answered in one video, great job explaining
In d), again, the first term is always a, =1 here. Then the subsequent term is always x times the previous, a geometric sequence whose series converges to 1/1-x, /x/
In b), don't complicate things. The original series doesn't need to be manipulated. Letting a=x^2 and r=x, the series equals a/1-r for/x/
swims she did a v good job ok, so pls leve her b!
Thank God the videos are only 10 minutes long, so i can watch all of them until my exam (TOMORROW)...
its now 7yrs later, did u pass?
In the example (d) you made the index substitution m=0, then m = n +1 which leads to the known solution for the Geometric Series 1/(1-x), It was nice. But, following the logic and method you used in example (b), we can factor the series (d) into sum (x * x^n) which becomes x * sum ( x^n ). Then the first term of the series we have now, which starts at -1, is 1/x followed by the Geometric Series. So, we get here x * ( 1/x + Geometric Series) = 1 + 1/(1 - x). This result is different, and better.
so who's rite fidel, u or she, cuz im caut in the middle!
Coolest Lady. I am getting interested in math again. Thanks a lot.Greetings from Germany.
*I watch math videos in bed every night to fall asleep*
very intuitive, d was a little tricky. If teachers were selected based on their ability to teach efficiently then there would be more lectures like this!
Nice explanations!
Nice. I am saving for future consultations
Suddenly I feel unstoppable
You explain better than my math teacher.
No wonder why they are the best in the world! All the other profss just talk nonsense to sound smart!!!
Beautiful.
I love how she handles that chalk
u perv.
POWER POWER POWER I HAVE POWER USING POWER SERIES.
THESE VIDEOS ARE AS POWER FUL AS POWER SERIES
You are excellent...it is great...please upload more videos..because I am not able to study in MIT.
An amazing teacher!
Thanks prof ❤
why e^x, is that belong to the integral form of x^n/x!? since the denominator is factorial so the derivative of e^x doesnt belong to this (the n can't be canceled out comparing to n with n! (factorial))
Can b also be written as the series of n = 0 to infinity of (x^2)/(1-x)?
Fantastic video
i just fall in love
It's assumed that was already known. x^n/n! is the known series representation of e^x.
Dear Christine, you have made a slight mistake regarding the infinite sum of your GEOMETRIC series (GS) in parts (b) & (c) etc. So let me try to correct it: GS is converges APPROXIMATELY to (1/1 - x), if and only if , the value of x is strictly POSITIVE and less than 1 (i.e. inside/within the OPEN interval (0,1)) . Do check it !!
KUDOS
Of course she said at the beginning don’t worry about convergence. No mistake made
For geometric series must be:
|X|
Hello there. I have a question about power series. can you help me
can someone explain for (a)? how x^n/n! = e^x? i got lost there.
Timothy Yeav this is a quick tip, it is integration of whole expression. You are gonna find the deduction in geometric series formulas.
can we have equations with series? using series in equ and find x?
Professor Jerison , how familiar name it is
Thank you so much.
You are like a tamil teacher
GREAT EXPLANATIONS. THANKS FOR MIT
wait, for A I don't get the e^x part. anyone please explain this to me!! :)
3422583 thank you!:)
Play the video in 0.5 speed.
You're welcome.
Loooooooool
Funny guy
5:10
Why did you subtract it? Shouldn't you added them instead?
subtract what Hot pepper einstein?
(b) only works if ¦x¦
she has mentioned twice in the beginning that x belongs to values which make the series converge
I’m assuming manipulations are good.
It's a matter of notation and preference. I would rather have my index begin at zero.
Math is all about testing ur reasoning power!
Infinity from sigma proof.
i almost pop off ... you should star by saying the geometrical series is valid between 0 and 1
STUDENTS NEED NOT DEPEND ON PROCESSORS.. THIS MIT VIDEO IS SUFFICIENT
I love you
W professor.
Quiero que ella sea mi profesora de Integral =D
yo tambièn J Alba
Mam are you Ph.D ?
what diff. does it make?
Nice! I like (d)
LOL
@yoyaya007
ROFL
Number operating system power solution grammar mathematics ensemble degree wordperfect alphabet.Allah.
*I watch math videos in bed every night to fall asleep*