Real Analysis 18 | Leibniz Criterion

[@Sci-Fi-Mike]

Thank you for the great videos! I'm watching this during breaks from reading and working on problems. I'm studying for an analysis qualifying exam. This has been very helpful!

[@brightsideofmaths]

Thanks! I am glad that my videos can help :)

[@anascimentopt]

in 6:38 there is a typo in the graph. The sequence S_2l+1 is monotonically "increasing" + bounded instead of "decreasing" as in the label used in the figure.

[@brightsideofmaths]

You are right. Sorry for the confusion!

[@anascimentopt]

Ok Sir. No need to ask for sorry! By the way. Are you going to post more videos about linear algebra? Also you mention in your page we can download your book about it (linear algebra I suppose). But I can't find the link. Is it available only for members?

[@Hold_it]

@@anascimentopt Maybe you have already found it, but if you are still looking, you will find it here : jp-g.de/Skripte/LA-GES-CS-JPG.pdf You should be able to get it even if you aren't a member.

[@anascimentopt]

@@Hold_it Dear Sir. Thank you very much in allowing me access to the book. Actually I did not find it before. So, once again thank you. All the best for you

[@remlatzargonix1329]

Thank you for doing these videos! Cheers!

[@qiaohuizhou6960]

2:15 alternating series test 3:09 proof

[@Deksudo]

Could you maybe do a Numerical Analysis playlist? There doesn't seem to be much english content on stuff like condition number, stability but german uni courses focus pretty heavily on it from what i see.

[@brightsideofmaths]

Very good idea! I really like to do that.

[@ahmedamr5265]

Thanks for the great video! Isn't it the case that the theorem requires the monotonic decrease of the sequence of only the absolute values of a_k?

[@brightsideofmaths]

Yes, you can tweak the assumptions like that in some sense. However, you still need that the limit is zero. In general, you need an alternating sum :)

[@ffar2981]

1:49, Is there a reason that use (k+1) instead of k in the exponent as is used in the Leibniz criterion? :-)

[@brightsideofmaths]

It's just multiplying by (-1). Not really a difference :)

[@YumeMiteru]

I have a question about series (-1)^(n + floor(sqrt(n))) / n. Will it converge by Leibnitz test? Our professor said yes, but I'm not sure

[@brightsideofmaths]

The question is only: can you apply the Leibniz test? :)

[@YumeMiteru]

@@brightsideofmaths I doubt

[@brightsideofmaths]

Why?@@YumeMiteru

[@yaseenbenrekia1095]

So great !!!

[@brightsideofmaths]

Thank you very much :)

[@nineinchbullet2875]

What's the dark side of mathematics?

[@brightsideofmaths]

A secret project of mine.

[@hemantpathak983]

Reading it one day before the end terms