Geometric Series | Convergence, Derivation, and Example
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- เผยแพร่เมื่อ 13 ก.พ. 2019
- 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.
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I regret that, I didnt start watching all of your videos before going to college. You don’t know how much this helps me.
Three weeks, after I realised it, but what if r = -1. You get something really strange its like nor diverging and nor converging. Im confused at this point.
@@abrahamsweetvoice7687 That is why you have an absolute value of r. In your case, |-1| is 1, so the sum diverges.
@@TheAS016 yeah. but r=-1/2 nothing bad!
at least you had the oopprtunity lol i graduated and he then makes these videos
5:07 this is the aha moment I needed. Thank you so much!
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!
How comes I’m just seeing your videos..... bro your the best
This was beautifully explained thank you so much
My best TH-camr of the year❤🎉
It also converges for a = 0
Top Tier Professor
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
excellent!
Thanks dude
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?
@@DrTrefor this is a great series and in general great channel. Thanks!
Hey Professor,
Which branch of mathematics is included sequence and series?
Typically it is introduced in calculus, but had applications in many fields like differential equations
@@DrTrefor Thanks
wait why can you take out the 1/2 and rewrite it @5:31?
Trefor Bazett thank you!
Could some please explain why at 5:00, (1/2)^n = (1/2) * (1/2)^n-1
(1/2) is (1/2)^1
I’m in 6 grade and this guy makes this sound so much easier than other people
Same I'm in 4th and this is a much better explanation then the one my teacher did using 300 melons
@@krizh289 same, am in kindergarten and really like this guy explains
@@jdavis2921gugu gaga, I'm only 3 and it looks easy to me👶🏻
Wondering can U actually multiply an "Infinite" series by a number such as r. How wuld U do it since it's infinite?
You do it by the distributive property.
Zeno paradox solved!
What if n start from 0?!
Ba ?
What about r=-1 ?
And a=0?
No problems, the series converges (as r
U said " if I wanted to go 1 unit away and then a 1/2...". It starts at 1/2, not 1.
1/2^0=1
Not the dot dot dot
thanks but why are you shouting im so exhausted watching this video in the middle of the night
He's just excited
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.
I appreciate that. I tell my students that my videos are designed to be watched by pausing and reflecting regularly, not full paced the whole way through. I'd try watching WITHOUT taking notes, pausing after a minute or two, and then formulating notes that make the most sense for yourself
U can literally rewatch things to process it thats what I do
@@DrTrefor Meanwhile I have ADHD and I watch lectures at 1.75x speed, lol. Everyone is different, that's why it's great that there's an option to change video speeds.
no way im passing this class