Sequences and Sigma Notation

In class on Wednesday, we learned about sequences and summation notation. By using sequences, one can determine the nth term when given a sequence of numbers.
Also, one can determine the sum of a set of numbers by using summation (sigma) notation. Here is a simple example:

The number at the top, 3, is called the upper bound or limit. The number at the bottom, 0, is called the lower bound or limit. In this case, n is the variable that will be used; as you can see, n is set to 0 to begin with.
The process of finding the sum requires you to substitute every value of n (in increments of 1) from the lower limit to the upper limit into the expression to the right of the sigma symbol.
For this example, we would start by substituting 0 (n's starting value) into the expression (2+3n). This yields:

2 + 3(0) = 2

We would repeat this process for every value of n until n was equal to 3:

2 + 3(1) = 5
2 + 3(2) = 8
2 + 3(3) = 11

Now, we take all of the numbers that we have produced and add them together:

2 + 5 + 8 + 11 = 26

Finally, we have determined that the sum of every number from 0-3 when substituted into the expression (2+3n) is equal to 26.