Imagine a supervillain kidnapping you except instead of someone evil it's just Dr Peyam and instead of holding you for ransom he just does math with you.
Precisely! Now what is interesting is what the difference between 1/n^2 and 1/(n^2 +1 ) konverges to? As both series konverge they must tend to a sum at infinity - the problem is now that the difference must tend towards a finite number. This holds true even if the two series diverge as the case is with the Euler-Mascheroni constant.
@@drpeyam Well it has some very real life consequences. The Gaussian integral is so very close to being a constant, that assuming something is normally distributed (without some additional argument) leads to disaster. F.i. there was a nobel prize given to a moron, that assumed that the stock exchange movements were normally distributed. Now they are not - that they obey any underlying basic assumption of being deterministic is indeed a dubious one - it might be true, but that does not mean that any old assumption pulled out of a hat is as good as any other - it isn't. It is contradicted by the repeated fact that stock markets crash every 30 years (i.e. in living memory of all the participants) - it is so regular, that it more probably is deterministic. This assumption of Gaussian integral totally ignores the existence of "fat tailed" distributions where unlikely events with a very high value. The event itself is unlikely but the consequenses are monumental. The important thing is here to know - what you don't know: th-cam.com/video/dhYxnL_Je7w/w-d-xo.html
Good Afternoon Sir, I am from India, Sir I want to know that what is the way to find the sum of the infinite series as if the series converges, where it converege? Or it all depends on the difficulty level of the question or we have any method or therom which will help us to find the sum?
Балет, вы задолбали уже называть видео Proof, Proof. Давайте уже как нибудь соберёмся и посасём друг у друга. Не вынуждай меня везде это писать убери эту хрень.
As the proof that series is 1/n^2 is convergent, we can use, that is convergent 1/(n*(n-1))=1/(n-1)-1/n
I like that!!! 😍
We can use too integral criterium😊
your lighting on the set = perfect lighting for a horror scene in a movie : )
I was thinking the same thing hahaha
The horror of sequences and series, right? (I do not think they are bad, but other people do)
Imagine a supervillain kidnapping you except instead of someone evil it's just Dr Peyam and instead of holding you for ransom he just does math with you.
You are apparently as captivated by mathematics as we are ... Saturday night ... and this is what we are doing ... hahaha ...
I know, right? 😂
If I did this correctly, I’m pretty sure that 1/(n^2+1) from n=0 to inf is (pi*coth(pi)+1)/2 as well. Wonderful!
Dear Dr. Peyam, isn't the Comparison test just the Squeeze Theroem for the special case where one of the bounding sequences = 0?
It is and this is the formalism of it
@@drpeyam thank you
brilliant video, really helped me study for a real analysis midterm, thank you so much!
Dr Peyam's knowledge is way beyond our understanding
Precisely!
Now what is interesting is what the difference between 1/n^2 and 1/(n^2 +1 ) konverges to?
As both series konverge they must tend to a sum at infinity - the problem is now that the difference must tend towards a finite number.
This holds true even if the two series diverge as the case is with the Euler-Mascheroni constant.
Great observation!!!
@@drpeyam Well it has some very real life consequences. The Gaussian integral is so very close to being a constant, that assuming something is normally distributed (without some additional argument) leads to disaster.
F.i. there was a nobel prize given to a moron, that assumed that the stock exchange movements were normally distributed. Now they are not - that they obey any underlying basic assumption of being deterministic is indeed a dubious one - it might be true, but that does not mean that any old assumption pulled out of a hat is as good as any other - it isn't.
It is contradicted by the repeated fact that stock markets crash every 30 years (i.e. in living memory of all the participants) - it is so regular, that it more probably is deterministic.
This assumption of Gaussian integral totally ignores the existence of "fat tailed" distributions where unlikely events with a very high value. The event itself is unlikely but the consequenses are monumental.
The important thing is here to know - what you don't know:
th-cam.com/video/dhYxnL_Je7w/w-d-xo.html
Great video what's that painting in the background?
Der Kuss by Klimt
Good Afternoon Sir,
I am from India,
Sir I want to know that what is the way to find the sum of the infinite series as if the series converges, where it converege?
Or it all depends on the difficulty level of the question or we have any method or therom which will help us to find the sum?
Why do you guys always use "sir"?
The light... i feel math devil or something is coming!!!
Ö
Wow youre clever men
Next time with complex analysis.
✌️😄
Балет, вы задолбали уже называть видео Proof, Proof. Давайте уже как нибудь соберёмся и посасём друг у друга. Не вынуждай меня везде это писать убери эту хрень.