Unit
Sequences and Series
University of Michigan
Runs his own tutoring company
Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
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University of Michigan
Runs his own tutoring company
Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
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.