Sigma Notation

If you have had experience with the Greek alphabet, then you may know that this letter is known as "Sigma." (The one you see is the uppercase version).  In math, there is something known as Sigma Notation, which is useful when wanting to represent large sums, without having to write it all out.  I'm going to give you an example, and see if you can figure out what it is trying to convey:

What does this mean?  Well, first of all we see 4 parts of the Sigma Notation.  The actual Σ, the i = 1, the 5, and the i.  The Σ means you are summing all the values up.  The i = 1 is your index, or where you start with your value, which doesn't always have to be i.  Then, the 5, is basically your limit, or where you stop adding the values once you reach that limit.  Finally, the i means that your are summing up each value as you go, or adding them together.  So what does this look like?: 

Does this make sense to you?  Well, let's go through the process again.  The index, or starting point, is equal to 1, so we write down a one.  Then, we check if we have reached our limit of 5, and see that we haven't, so we write down a two.  You keep going through this process until you reach the limit of 5, and then you add all of the values together to get..... 15.  Sigma Notation isn't always going to be this easy, but this is just to start.  I'll give you another example.:

So, what are we going to do with this?  Well, we are going to replace each k, with a 1, so we get 1^2 + 1.  Then, we are going to do that, until we reach our limit of 5, adding each of the parentheses together.  What do we get?:

That's pretty big!  As you can see, the answer is 70, and I hope you got that.  Thank you for reading my first post, and I hope you learned something new today!