SEQUENCES CONVERGENCE TO DIVERGENCE HOW TO
SEQUENCES CONVERGENCE TO DIVERGENCE PLUS
SEQUENCES CONVERGENCE TO DIVERGENCE SERIES

So you can't use n equals one to get five. You're usually trying to relate the index to the number that's produced the index to the and it has to be the corresponding number in the sequence. So when you're trying to find the formula for a sequence, you're trying to relate the index. It's the relationship between your index and the number that's produced from the formula. You can tell when you're writing out this list. And this function that's inside the brace right here. The one would be your N equals one term and equals to term and equals three terms. So this sequence would be represented by one to three, four five and it would keep going on forever. Could be you could just have in we're in equals one to infinity. Five term would be eight and this would be the end of our sequence. The N equals two term and equals three terms and equals.

SEQUENCES CONVERGENCE TO DIVERGENCE PLUS

Three plus four is seven, so this would be an equals one. Three plus two is five three plus three of six. So what this would look like three plus one is four.

Let's say we have three plus in we have n equals one up to five.

SEQUENCES CONVERGENCE TO DIVERGENCE SERIES

You put your formula in the brackets or braces, and you have that n equals sub number, which would be your starting number, and it goes up to infinity, which would mean it's an infinite series that keeps going on, or you could end the sequence at a number. The alternative way to represent a sequence is with bracket.

If it's infinite, a sub right, so it'll keep going. So so far we've talked about a sequence that's a seven, and it's represented by a one a two a three dot dot dot. They're also called index Okay, the alternative way. Sometimes we might have to solve Okay, so those sub scripts are very, very important those indexes. So the sub scripts on A This becomes really important when we talk about the recursive sequences subscript on a are in or related toe end in some way. if it ends, all we're given is a formula, Okay? Eso One thing that's really important to note this one, these sub scripts, that's what end is in the formula. If you put those dot dot dots, that means we're looking at an infinite sequence, a sequence that we do not know when it ends. And your sequence would be two comma, four comma six and then this one would keep going, right. Your third term would be two times three, which would give you six. So this would be four would be your second term ace of three. So your first term would be to your second term and is now too. That means everywhere you see an end, you're gonna plug in a one. For a simple one ace of one, that subscript run represents your first term. So let's say you're typically gonna have some a sub in which will be equal to some formula. Okay, so now that we have that, let's look at a common what? I mean, like this.

SEQUENCES CONVERGENCE TO DIVERGENCE HOW TO

We're gonna look at how to find these formulas as well. What we're working with that is usually going to be the case in the formula that defines the sequence.

Not every sequence has to be defined by a formula. So this is also worth noting in the formula that defines the sequence. So the index tells you what term you're looking at, and the other important thing to mention is N is usually involved in the formula that's used to find the sequence. So if we say we want the A sub third term, we would look at a sub three. Those sub scripts on the A's are referred to as the index. So the one the one the two, the three before and then all the way to the end. So this is what a sequence would look like a someone's air, the numbers we call those sub scripts. So what this looks like is you'll have some number 81 a two a three a four and then it would keep going, and it might stop it. So a sequence is basically numbers, um, that air, separated by commas on the separated by commas part is going to be important when we talk about Siri's and what the difference is between a sequence in a Siri's so sequence air numbers separated by commas. Okay, We're going to start our lecture on sequences.

Sequences convergence to divergence