Sequence and Series

Definition of Sequence- An infinite sequence is a function whose domain is the set of positive integers. The funciton values

are the terms of the sequence. If the domain of the functioning consists of the first n positive integers only, the sequence is a finite sequence.


Finding the Terms of a sequence





The Fibonacci Sequence: A Recursive Sequence

Definition of Factorials- If n factorial is defined by

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

• 0!=1



• 1!=1



• 2!=1 x 2 = 2



• 3!= 1 x 2 x 3 = 6
  
  
  

Evaluating Factorial Expressions

Definition of Summation Notation- The sum of the first n terms of a sequence is represented by

Where i is called the index of summation, n is the upper limit of summation, and 1 is lower the limit of summation

Sigma Notation for Sums