Series and Summation Notation - Concept
An important part of understanding functions is understanding their domain and range. Domain and range are all the possible x-values and y-values of the function, and can often be described easily by looking at a graph. In order to grasp domain and range, students must understand how to determine if a relation is a function and interpreting graphs.
So a series is just the summation of a sequence. So a sequence is just a bunch of numbers in a row, a series is what happens when we add up all those numbers together. Okay?
So before me I have a general term for a sequence. a sub n is equal to n squared minus 1. And first we're asked to find the first four terms. Okay? So in order to find the first term, we would find a sub 1 which happens when we plug in 1. 1 squared minus 1 that's just 0. So our first term is going to be 0.
To find the second term we plug in 2. a sub 2 is equal to 2 squared. 4-1 which is going to give us 3. Third term [IB] and repeat a sub 3 is 3 squared, 9-1 is 8. And the fourth term a sub 4, plug in 4. 4 squared, 16-1 is 15.
So this right here is a sequence. It's 4 numbers written in order with commons in between. It's just a collection of numbers.
Find the sum of those first 4 terms. So basically we already found the 4 terms, all we have to do is add them together. 0+3 is 3 plus 8 is 11 plus 15 is 26. So 26 is then the series, okay? Series is the way I remember it is, series is a shorter word therefore your answer should be shorter, one number. A sequence is a longer word, it's going to be a collection of data, a collection of numbers, okay?
So basically all the series is is a summation of the sequence.