Section 9.1 Sequences, Series, and Probability part 2

In this section we will discuss summation notation.
              Summation notation is also known as sigma notation because it involves the use of the upper               case Greek letter sigma, written as .

Definition of Summation Notation

          i is the index of summation
          n is the upper limit of summation
          1 is the lower limit of summation
               
                  Example:

Properties of Sums

1. c is any constant

2.

3. 

Series

An infinite series or simply a series involves the sum of the terms of an infinite sequence.

Definition of a series

              Consider the infinite sequence

              1. The sum of all terms of the infinite sequence is called an infinite series and is denoted by                                                     

              2. The sum of the first n terms of the sequence is calls a finite series or the nth partial sum                                     and is denoted by.

Example

              The 3rd partial sum of.

              The sum of the series is