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Geometric Convergent vs. Divergent - Overview

In mathematics, a convergent sequence is a sequence of real or complex numbers that has a finite limit, i.e. that has a real or complex value that the sequence tends to as the number of terms increases without bound. The terms of a convergent sequence are said to be "converging" to this limit. A sequence that does not converge is called a divergent sequence. The limit of a convergent sequence is also called its sum. The value of a convergent sequence is also called its sum even when the term "sum" is not otherwise used in the context.

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Video Transcript

Okay, So in this video, we are going to be discussing Convergent versus Divergence Siri's. So for a conversion versus divergent, let's first define those terms so convergent when something converges, that means it comes together. So for the purposes of math, we know that it comes together to like, kind of one point. So you basically, any time you find a limit, that's what it's doing is it's going towards one point se towards a point. So then diversions, as you can guess, is going to be the opposite, meaning that it does not come together towards the points, and in fact, it goes away. So, um, if I were to give you some graphs, convergent would be something where we have would have it coming towards maybe zero or if it's going like this, something like that, that would be converging. Diverging would be where we have something going like out like this out like this, or even in some situations. We can have it go like this and go out like that, get bigger and bigger towards each extreme, so those are kind of graphically what we can have if we have a convergent or divergent. Siri's So then let's think about well, how do you know when something is convergent versus divergent? Well, we know something is convergent so convergent when the absolute value of the art is less than one. And so for the divergent, we know something is divergent when the absolute value of the R value is greater than one. So then people might ask, Well, how do we determine what the R value is in a geometric? Siri's? Well, So here's the thing again. What the Geo conversion versus type version. If this question is being asked, then you know you're dealing with geometric Siri's because all arithmetic So all arithmetic serious, converge or diverge. Sorry, meaning there because it's linear because arithmetic Siri's you're adding the same amount each time or subtracting the same each time. It's linear, so it's always going like this or like this, like this, like this. So it's always die approaching. So then, for a geometric Siri's, it can converge or diverge because you're multiplying by something. So then, with the R value, you can obtain the R value by taking the term over the term before it, so you would say Jesus end divided by the Jesup ed minus one, which is a term that came before it. And then you basically just use that and look at it to see whether it's going to converge or diverge, Yeah.