Sequence & Series

Success Criteria

At the end of this chapter, students are able to:

1. Use the summation notation to denote a series.

2. Find the sum or difference of two series.

3. Find the sum of a series using the method of difference.

4. Formulate the general term of an arithmetic series.

5. Find the partial sum of an arithmetic series.

6. Formulate the general term of a geometric series.

7. Find the partial sum of a geometric series.

8. Determine if a geometric series is convergent.

9. Find the sum to infinity for a convergent geometric series.

Definitions

A sequence is a list (Ordered) of numbers (Terms). An example of a sequence are the Fibonacci numbers = { 1, 1, 2, 3, 5, 8, ... }. A sequence may have repeated terms compared to a Set in which every elements is unique.

The length of a sequence is the number of terms in the sequence. 

A finite sequence has a finite length whereas an infinite sequence goes on forever.

A series is the addition of terms in a sequence.