Estimating the Remainder of a Series Approximation via the Integral Test

If we approximate a series by a partial sum, how good is this approximation? In this video we modify the argument used in the Integral Test to come up with a formula that creates a bound on how bad the "remainder" or "error" of this approximation can be. That is, the remainder will need to be less than a particular improper integral
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This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati.
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[@mario64onstarcraft]

This man is a professor at the university I'm attending. My eyes nearly popped out the sockets when i passed him in the halls. Small World huh

[@englishlife5838]

Please do not dislike this video. The best explanation ever!

[@김신-v5v]

This lecture is just so awesome. Thank you sooooo much I love you❤❤

[@quriositysquared1028]

I was completely confused about the whole infinite sequences and series bit. Your playlist is amazing. Thank you!

[@albertotosetto5089]

Best professor ever. I am really Grateful. That is the why I like internet. I can learn from different places. Intersting.

[@DrTrefor]

Thanks! 😃

[@expansion_forever]

Excellent explanation

[@hasaniqbal233]

whyyyyyy can't they just teach it like this? Why does my university, supposedly the "best" one in Canada, have teachers who can't explain this?!? Thanks for making this so easy

[@mihirsolanki1897]

You're a life saver!!
Thanks a lot!!!

[@DrTrefor]

You're welcome!

[@maxpercer7119]

Starting at around 3 minutes, using your graph animation you simplified a lot of painstaking reading when finding bounds for the remainder.

[@heroess4766]

thank you for this wonderful video sir

[@boaozhang7188]

Thanks! This really helps!

[@rohannaik1822]

Thanks! really helpful

[@DrTrefor]

Glad it helped!

[@muditasai6412]

Thank you so much!!!!!!

[@DrTrefor]

You’re most welcome!

[@hmudisalam]

wonderful :)

[@pandie4555]

Thanks!

[@shadon_official2510]

Thanks

[@duckymomo7935]

What is O(x^3) for example?
Sin x = x + O(x^3)
I heard it called as asymptotic notation
Is it related to error/remainder?

[@chinabot6954]

@ 4:04 sadge

[@deshithadhananjaya3122]

until now there is no any dislike... wowwwww

[@multipledone7501]

what are the daily use of applications of Integral test.