9.1 Sequences and Series

In 9.1, we learned about sequences and series.

Sequences

A sequence can be defined as:





EXAMPLE: Finding terms in a sequence

           Start with the equation for the sequence


 

Plug in the numbers to solve
               



EXAMPLE: Finding the nth term in a sequence

                         Take the terms given and compare them to the term number

Then try to find a pattern. For this example, the pattern appears to be

A special type of sequence is something called a Fibbonacci Sequence. This sequence is recursive, so it uses the term prior to itself to continue the sequence.


An example of a Fibbonacci Sequence


       

where   

     Add the previous 2 terms together
   By doing this you can find the terms in a Fibbonacci sequence

       

Factorial Notation

Definition:

If n is a positive integer, n factorial is defined by

 

As a special case, zero factorial is defined as 0!=1

1!=1
2!=2
3!=6
4!=24
and so on...

Now to evaluate a factorial expression, you can divide like factorials out. here is an example...

 Start with given equation

  You seperate the 8! into that because that way it is easier to simplify since the two 6! divide out

 Then simplify

And you get your answer!