Geometric Series | Convergence, Derivation, and Example

The Geometric Series is one of our foundational series. Unlike most series we will se in Calculus where we can determine convergence but not what it actually converges too, for the Geometric Series in fact we not only know exactly when it converges, but also what it converges too.

****************************************************
YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems!
****************************************************

****************************************************
Other Course Playlists:

***************************************************

► Want to learn math effectively? Check out my "Learning Math" Series:

►Want some cool math? Check out my "Cool Math" Series:

*****************************************************

*****************************************************

*****************************************************

This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati.

BECOME A MEMBER:

MATH BOOKS & MERCH I LOVE:

[Caleepo]

I regret that, I didnt start watching all of your videos before going to college. You don’t know how much this helps me.

[MrCEO-jwvm]

Thanks so much, Dr. Bazette. You've opened my mind to the beauty of series, which for years now looked really abstract without understanding. This playlist is so rich and well-delivered. Thank you so much because this confirms that I'm on the right path to majoring in math!

[Lucas-sklu]

5:07 this is the aha moment I needed. Thank you so much!

[emilyboyle]

This was beautifully explained thank you so much

[charliecho]

such a legend of a math teacher you are..

[alforex]

How comes I’m just seeing your bro your the best

[idk-osx]

Great detailed and concise introduction to convergence and divergence of geometric series.

Excellent.

[christianbrown]

the only part that confuses me is why would the geometric series case of convergence be different than the harmonic series? It seems like the numbers in harmonic are getting infinitely smaller to the point that they are a rounding error, but yet they still diverge. In your harmoinc video it makes sense via the comparison test, but I don't understand how it makes sense when we think about it in terms of it getting infinitely smaller until the subsequent numbers are inconsequential. Thank you

[vincemcman]

What is meant by "Ill never get that one unit away, Ill only get half of the unit away..." Does that mean in Ex 2 that you are actually closer?

[ethanvirtudazo]

Could some please explain why at 5:00, (1/2)^n = (1/2) * (1/2)^n-1

[maddy]

wait why can you take out the 1/2 and rewrite it @5:31?

[tasninnewaz]

Hey Professor,
Which branch of mathematics is included sequence and series?

[danielrosen]

Wondering can U actually multiply an "Infinite" series by a number such as r. How wuld U do it since it's infinite?

[jadeqochaini]

I’m in 6 grade and this guy makes this sound so much easier than other people

[davidrosenman]

U said " if I wanted to go 1 unit away and then a 1/2...". It starts at 1/2, not 1.

[frenchmike]

everything is high quality but i can never comprehend you cos u run through everything so fast. yes i know i can play it slow motion but i shouldn’t have to. i mean i wonder if u would be happy to learn math from a teacher who just run through everything this fast. no time for the brain to process.

[herseycokanlamsiz]

thanks but why are you shouting im so exhausted watching this video in the middle of the night