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Write the sum using sigma notation:4+6 + 8 + 10 ++ 26B, wheren =A =B =Question Help: QVideo @Video OMessage instructorSubmit QuestionJump to Answer...

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Write the sum using sigma notation:4+6 + 8 + 10 ++ 26B, wheren =A =B =Question Help: QVideo @Video OMessage instructorSubmit QuestionJump to Answer

Write the sum using sigma notation: 4+6 + 8 + 10 + + 26 B, where n = A = B = Question Help: QVideo @Video OMessage instructor Submit Question Jump to Answer



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Write the given sum using sigma notation. $$ 2+6+10+14+\cdots+38 $$

All right, sir, our job here is basically to write this in Sigma Notation or with that summation sign. And first we have to see what's happening here. And it's a pretty easy pattern to see we're adding three each time that first, we kind of got cut off, but adding three each time, pretty easy pattern to see in the way that you represent. This is usually by doing a three multiplied by an end sort of thing. But we gotta recognize where we start as well in the place that we start right here is that too. So I start with two and then I add three on forever. Never Essentially. So I do too, plus three and add three in amount of times. Now, one more thing we have to be careful of is we want to make sure that this first term doesn't have three added to it. And it's pretty simple to do that. You just say n minus one. And the reason we do that is if I plug in a one here, one minus one is zero. That's gonna make sure I don't add a three on that first term. But for that second term to minus 10 that gives me that one. Exactly. 13 to be added here. Good. And so there is your summation. You're going to start with n equaling one. And now we just have to figure out where we end. And what might be tempting to do this? You could just say, Oh Oh 29 minus two is 27 and 27. Divided by three is 90 I must be adding nine terms. You actually have to remember this end minus one thing going on here. And so it's actually that 10th term is the one. We're going to stop that. If you want to plug that in with me toe check. If I plug in 10 minus one, that's 99 times three is 27 27 plus two. Is that 29 that we want to end that? So there is our term in summation notation or signal notation. Right there.

Hello. So here we are, given the somewhere we have two plus four plus six plus eight and so on. This pattern continues all the way up to plus 50. Okay. So what is the pattern here? Well this is just the sum of all the even numbers Going from 2 to 50. So therefore that can be written as the sum where we have I um going from. Well we start at let's say one and then there's gonna be 25 terms here. So I is going from 1 to 25 of what we'll just of two I.

Okay, so we want to write the falling eyes of some. Well, let's note that that's just the some from 1 to 11. So it's what any people to one and then we have and be here, and it's all the way up to 11.

Okay, so let's know that our first term is it too. Why don't we rewrite this as a to over one? So it follows our next time. Notice that we have a one and then a one plus one, which is a to and our next time is a two and a two plus one. So we can write this Oz one plus 1/1 comma, two plus 1/2. So it's so set. These are our terms that are changing. Macedo are starting. Value is a to And what about our last term? That would be a nine plus one over a nine on our ending Value is a nine. So let's write this as a summation from an ethical to one to a nine of and plus one all over and


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