16:21 Or maybe -1/12. (Who am I to argue with Ramanujan?) Just like the product of all positive integers is sqrt(2 pi). Edit: oh, you're starting with k=0, not k=1? For maximal confusion, that really can make a difference. Second edit: going from the Wikipedia article on 1+2+3+4+..., changing f(x)=x to f(x)=x-1 should add +½ to the sum, resulting in the new sum 0+1+2+3+... = +5/12.
7:50 is infinite series a sum? like infinite series is just one number(sum of ak's)? aren't series(in general) seperated by comma? like 1, 1/2, 1/3,1/4, 1/5,...... instead of 1+1/2+1/3+1/4+1/5+.......( which would just give one single number). How is the latter one a series if it is giving us the sum?
Thanks for watching and for the question! You're thinking of sequences: th-cam.com/video/YEiZWonJrOg/w-d-xo.html A series is a sum, so if the series is convergent then it is equal to just one number. It may not be convergent though. It may diverge to infinity, negative infinity, or just jump around chaotically.
@@WrathofMath there are some books which says series is a special kind of sequence general by the use of partial sums of a given sequence. Reference: Introduction to Real analysis by Robert G. Bartle. Let me know is I get something wrong.
If we are assuming half of distance to be 1/2 (whole distance divided by 2) does not that mean that full distance is 1 (Oneeeeeeee). What an irony of mathematics. if we assume whole distance to be 2 units than half distance would be 2/2 :D .
![TIMETHAI - ไม่อยากให้เป็นเขา (Why tho?) [OFFICIAL MV]](http://i.ytimg.com/vi/o2qYlGVVtOw/mqdefault.jpg)
Much more on infinite series to come in my Real Analysis playlist! th-cam.com/play/PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli.html
Please I'm not able to watch this video
I'm 100% sure that I would have given up self studying analysis without this real analysis series! best videos on the topic hands down
Really appreciate that, thank you! Looking forward to completing it some day soon!
3 years later this helped me explain infinite series on my precalculus final (8 page paper) wish me luck. I COULDNT HAVE DONE IT WITHOUT THIS VIDEO!!!
Y… you are doing series in pre Calc?
What’s your major I’m scared
Infinitely useful!
Thanks for making this video it helps me a lot!
So glad to hear it, thanks for watching!
16:21 Or maybe -1/12. (Who am I to argue with Ramanujan?) Just like the product of all positive integers is sqrt(2 pi).
Edit: oh, you're starting with k=0, not k=1? For maximal confusion, that really can make a difference.
Second edit: going from the Wikipedia article on 1+2+3+4+..., changing f(x)=x to f(x)=x-1 should add +½ to the sum, resulting in the new sum 0+1+2+3+... = +5/12.
Very good!👍
Good video!
Thank you!
Hight quality vedio thanks a lot
thanks so much!
so useful!
I tried to make it as useful as I could!
This video is given😊❤
Thank you!
7:50 is infinite series a sum? like infinite series is just one number(sum of ak's)? aren't series(in general) seperated by comma? like 1, 1/2, 1/3,1/4, 1/5,...... instead of 1+1/2+1/3+1/4+1/5+.......( which would just give one single number). How is the latter one a series if it is giving us the sum?
Thanks for watching and for the question! You're thinking of sequences: th-cam.com/video/YEiZWonJrOg/w-d-xo.html
A series is a sum, so if the series is convergent then it is equal to just one number. It may not be convergent though. It may diverge to infinity, negative infinity, or just jump around chaotically.
@@WrathofMath there are some books which says series is a special kind of sequence general by the use of partial sums of a given sequence.
Reference: Introduction to Real analysis by Robert G. Bartle.
Let me know is I get something wrong.
@@Rsingh1 any series can be seen as the sequence of is partial sums.
If we are assuming half of distance to be 1/2 (whole distance divided by 2) does not that mean that full distance is 1 (Oneeeeeeee). What an irony of mathematics. if we assume whole distance to be 2 units than half distance would be 2/2 :D .