Slide 2:
Series: the sum of the terms of a sequence
Sn = a1 + a2 + … + an
Since many sequences are infinite, it if convenient
to consider the sum of only a finite number of terms.
This is a partial sum (Sn).
Given 1, 3, 5, 7, …, find S1, S2, S3.
S1 = 1
S2 = 1 + 3 = 4
S3 = 1 + 3 + 5 = 9
Slide 3:
Sigma Notation:
The Greek letter can be used to simplify notation
When the series has a formula for the general term.
The formal for sigma notation is as follows:
Slide 4:
Expand and evaluate.
1. You will first need to find the terms of the sequence.
Substitute the numbers 3 – 6 into the function:
3 + 1 = 4
4 + 1 = 5
5 + 1 = 6
6 + 1 = 7
The sigma denotes addition so 4 + 5 + 6 + 7 = 22
Slide 5:
2.
Substitute the numbers 2 – 5.
3(2) + 1 = 7
3(3) + 1 = 10
3(4) + 1 = 13
3(5) + 1 = 16
Add. 7 + 10 + 13 + 16 = 46