Power Series

We've gone through a few different types of series, so let's learn another type, power series. What are these, and how can we tell if they will converge or diverge? The ratio test is back!

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[KidNamedVashin]

Can you do a tutorial on how to fix my life?

[laeclorentzen]

This is the first explanation of power series that has made sense to me: and two hours before my midterm, too! 😂 Thanks.

[Miner_Experting]

Thanks dave, you litterally saved me a good hour trying to learn this

[madykz]

Professor Dave, you saved my life throughout the entire Chemistry series I never knew I'd be so lucky to get your help in math too! Thanks for making these videos, you're my hero!!!! <3

[tamarakalanda]

Professor Dave, your videos are so golden, in my opinion, since it’s:

- so clear (not to much just the perfect amount)

- precise (you detail all the steps even the same ones that you’ve already explained in older videos)

- simple (step by step)

- interesting ( explain the story and the object behind it).

I can’t thank you enough but I’ll make sure to recommend your videos to my friends doing those kind of subjects. Thank you again! (Sorry for my English my first one is French)

[nadyamarinova]

I have this "Ahhh, now it makes sense" feeling every time I watch your tutorial video! Thank you!

[manwithstds]

This 5 year old video is better than most of the other videos I found. Thanks Dave. You're the besy

[amarjitrohit]

Sir in second one the interval will be only (0, 2).not close interval na. As it is divergent also at 2

[coder-c]

Wow this explanation blew my mind the textbook over complicated it. Ty Professor Dave 👍

[rajarshinath]

One of THE BEST Math Teachers I've ever seen

[davidzimler]

At 5:28 you switched the interval. It should say (negative infinity, positive infinity).

[hyperspam]

In 6 minutes covered an hour and a half worth of lectures. And much more clear.

[SoYuan]

6:04 may I know why is the interval of convergence is (0, 2], not [0, 2]? If x=0, won't the series converge to 0? Thanks, great video!

[abdullahsheikh]

I did not get how to determine radius of convergence but i understood how to find the interval

[emanuellunnergard]

This was really helpful! Thank you! :)

[kenthartig]

Why are the intervals of convergence closed if we're using a "less than" rather than a "less than or equal to"? Why does this not apply to the second example? I'm a bit confused on that part.

[bao]

In checking comprehension, why in the first question the interval was inclusive?!
Also in the second question when I did the ratio test the limit went to infinity whatever the value of x! how comes (0, 2]? and if true why one limit is inclusive while the other is exclusive?

[jcwarain]

Aren't we supposed to check the convergence of the endpoints of the interval?

[monzirabdalrahman]

Thanks A lot professor... Wonderful explaining

[luiswimmer]

is it possible to take advantage of an infinite series and estimate the area under complicated integral?