You know how you learn to add numbers in kindergarten or first grade? It is very basic and easy to learn. Although it is a topic that comes very early in learning, even calculus uses the concept of addition. Did you know that the sum of numbers means to add them together? Well, summation, is kind-of like sum.
ISAIAH LOPEZ
Summations are used to express adding larger quantities together. For example, If you wanted to say 1 + 2 + 3 + 4 and so on, all the way up to ten, you could use the summation notation. The notation for summation is the sigma, which is a letter in the Greek alphabet. You can write 1 + 2 + 3 + 4 +...10 like this:
The "i" stands for the index. The number at the bottom of the sigma is the index starting value and the number at the top is the ending value. Since ten is at the top and one is at the bottom, you have to sum up all the numbers from one to ten. You might be wondering what the side value is. It just means what you want to do to each value. If you just have an "i" you will have to sum up all the numbers without doing anything to them. If you have, for example, "2i" you would just multiply each number by two, so it would mean 2(1) + 2(2) + 2(3) + 2(4) + 2(5), and so on, all the way until you reach ten. You could do whatever you wanted to to the value of the index. Here is an example:
In this example, the index value starts at one and ends at four. That means you sum up the numbers from one to four. There is one minor exception: you have to make each value 2(i) squared divided by i. (2(1))²/1 + (2(2))²/2 + (2(3))²/3 + (2(4))²/4 is what the notation above really means.
I hope you understand the concept of summations now. Another thing to keep in mind is that the top summation value could even be infinity. The best way to make it though is to have a fraction. If you want to see an example of that, check out my other article, What "e" Really is. So, to sum it up, summations are just addition, but expressed in a slightly different way.