I actually had no trouble dealing with the second term, but for the first term i did not realise that i can simply decide to choose a large n and make the entire thing small. Smart observation!
All these terms are GTSimplex so geometrically forms patterns and locked sets are formed which generates great dynamic geometries for different values of x
We started the problem by saying that (an) converges, so by definition for an arbitrary epsilon bigger than 0 there exists a N, where for every n> N. |an-L| < e. That all comes from just the definition of a convergent sequence, that's why for every An where n>N |an-L| is each smaller than epsilon.
well we will want to make it smaller than epsilon/2. Notice the numerator does not depend on little n, it's just a number really,a constant, so we have (constant)/n, so we can choose n big enoguh so (constant)/n < anythingwewant, that's the archimedean principle basically, so we choose epsilon/2 because that way the other one will be less than epsilon/2 also and they add to epsilon
Does this work for sequences that are elements of the complex numbers as well? Or would you need a different approach, I'm always a little bit confused as a beginner what you are allowed if it comes to complex numbers and what not.
This is not a bad video, but you could have improved the quality of the explanation by using Sigma notation to express the summations, since I definitely know some people could get confused otherwise. Preferrably, you should make a video about Sigma notation if you have not already. It makes proofs far neater and often much easier to understand.
I'm not sure advanced calc uses that notation. This is constructed in a way that uses definitions as they would appear in that course. Fyi wikipedia also makes no reference to sigma in the Cesaro summation page.
@@sharkofjoy en.m.wikipedia.org/wiki/Cesàro_summation Yes, it uses Sigma notation in the Definition section twice. Why do people like you who are so willing to lie and spread misinformation exist? You know it literally took me 10 seconds to fact check your claim, right? You should be ashamed of yourself.
I'm taking real analysis this year and this video was exceptional in helping me understand the problem. Thanks.
I actually had no trouble dealing with the second term, but for the first term i did not realise that i can simply decide to choose a large n and make the entire thing small. Smart observation!
Thanks a lot for such a clear explanation. I wish profs in Universities would explain everything as understandable as you
Thanks, I didn't know how to deal with that pesky constant term. Clever argument.
All these terms are GTSimplex so geometrically forms patterns and locked sets are formed which generates great dynamic geometries for different values of x
@The Math Sorcere Great video, thanks! Could you please explain 4:43-5:20? I don't. understand how you derive the inequality...
Can't wait for analysis class!
thank you for the clear explantion
Can you explain the epsilon decided by 2 concept?
At 9:42, little n is bigger than N1 but smaller than N2
There's a short track on Tool's Ænima album named Cesaro Summability
Oh wow that is cool!
sorry, i'm having a hard time understanding what happened to you n and why we subtracted L from each item
THANK YOU!! You were so clear.
hey i am glad it helped!!!
this makes sens now, thank you dear friend
hey np!
Why are the terms (a subN+1 - L) +...+ (a subn - L) each smaller than Epsilon?
waiting for an explanation too...
We started the problem by saying that (an) converges, so by definition for an arbitrary epsilon bigger than 0 there exists a N, where for every n> N. |an-L| < e. That all comes from just the definition of a convergent sequence, that's why for every An where n>N |an-L| is each smaller than epsilon.
Thanks, made a lot of sense.
Megaaaa FFFFFF I watch your videos a lot and this was on my test 😭😭😭😭😭😭
Nooooooooooooooooooooooooooo!!!!!!!!
pretty hard test question:)
can someone explain 2:59 to me. i dont understand why thats smaller than epsilon/2
well we will want to make it smaller than epsilon/2. Notice the numerator does not depend on little n, it's just a number really,a constant, so we have (constant)/n, so we can choose n big enoguh so (constant)/n < anythingwewant, that's the archimedean principle basically, so we choose epsilon/2 because that way the other one will be less than epsilon/2 also and they add to epsilon
Does this work for sequences that are elements of the complex numbers as well? Or would you need a different approach, I'm always a little bit confused as a beginner what you are allowed if it comes to complex numbers and what not.
Thank you so much. :)
:)
I like your ID picture.
i love you
Cheers m8!
cheers!
This is not a bad video, but you could have improved the quality of the explanation by using Sigma notation to express the summations, since I definitely know some people could get confused otherwise. Preferrably, you should make a video about Sigma notation if you have not already. It makes proofs far neater and often much easier to understand.
I'm not sure advanced calc uses that notation. This is constructed in a way that uses definitions as they would appear in that course. Fyi wikipedia also makes no reference to sigma in the Cesaro summation page.
@@sharkofjoy en.m.wikipedia.org/wiki/Cesàro_summation
Yes, it uses Sigma notation in the Definition section twice. Why do people like you who are so willing to lie and spread misinformation exist? You know it literally took me 10 seconds to fact check your claim, right? You should be ashamed of yourself.
bofsh hajer