This video will talk about how to use the summation symbol. But before I do that, I'm going to give you one of my favorite math jokes. That is, the squared of negative 1, 2 to the third power, the summation symbol, and then the symbol for pi. Or, I ate some pi, translated to English, I ate some pi, and it was delicious. Alright, but we're actually here to talk about the summation symbol. This is the summation symbol. It is the capital Greek letter sigma, and it means either summation or addition. We never use the sigma symbol by itself. We never use the summation symbol by itself. At the bottom of the summation symbol will be an index. In this case, I'm using the variable k. And we'll give a starting value. I could start at 0. I could start at 1. I could even start at negative 10. But I'm going to start at 0 for this example. On the top of the summation symbol will be another number, and that's going to be where we're ending our summation. It could be a variable n. It could be a number like 10, and it could even be infinity. But we'll leave it at n. And then we also have an element x sub k. Different elements based on the index that we're sequencing through. Again, k is our index. It does not have to be k. You'll see i, sometimes you'll even use n. In this case, we're using a k. We've got our starting value. And then at the top we have our ending value. And again, our element. Let's look at an example. This is the summation from k equals 0 to 4 of k squared. So what does that equal? Well, first we let k equals 0. Then we increase k by 1 to 1. Then we add another 1. And now we have 2, 3 until k is equal to 4. And at that point we stop because our lowest value is 0. And our highest value is 4. Now we just go ahead and evaluate the elements. 0 squared is 0. 1 squared is 1. 2 squared is 4. 9. 16. And when I add these all together, I get that the summation from 0 to 4 of k squared is equal to 30. Let's do a different example. This is the summation from n equals 0 to 4 of negative 1 to the nth power divided by 1 plus n. Again, in this case, I'm using the index n. It really doesn't matter as long as I'm consistent throughout my summation. You might want to pause the video and see if you could come up with an answer for this before I go ahead and give you the solution. And here's the solution. We first let n equal 0. Then we let n equal 1, 2, 3, and then 4. And what happens in the numerator is we have negative 1 to the 0th power. Well, anything to the 0 power is 1. But negative 1 to the 1st power is negative 1. But negative 1 squared is going to be positive 1, et cetera. So we'll have our numerator sign alternate between positive and negative. And then our denominator went from 1 plus 0 to 1 plus 1 to 1 plus 2, et cetera, until 1 plus 4. When I put these in terms of a common denominator and add them up, I get that the summation from n equals 0 to 4 of negative 1 to the nth power divided by 1 plus n is equal to 47 divided by 60. And that's about all you need to know to be able to calculate some actions.