CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 12. Discrete Math

12.3 Sigma Notation

Here you will learn how to represent the sum of sequences of numbers using sigma notation.
Writing the sum of long lists of numbers that have a specific pattern is not very efficient. Summation notation allows
you to use the pattern and the number of terms to represent the same sum in a much more concise way. How can
you use sigma notation to represent the following sum?
1 + 4 + 9 + 16 + 25 +···+ 144

Watch This

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/62273

http://www.youtube.com/watch?v=0L0rU17hHuM James Sousa: Find a Sum Written in Summation/Sigma Nota-
tion

Guidance

Aseriesis a sum of a sequence. The Greek capital letter sigma is used for summation notation because it stands for
the letterSas in sum.
Consider the following general sequence and note that the subscript for each term is an index telling you the term
number.
a 1 ,a 2 ,a 3 ,a 4 ,a 5
When you write the sum of this sequence in a series, it can be represented as a sum of each individual term or
abbreviated using a capital sigma.

a 1 +a 2 +a 3 +a 4 +a 5 =∑^5
i= 1

ai

The three parts of sigma notation that you need to be able to read are the argument, the lower index and the upper
index. The argument,ai, tells you what terms are added together. The lower index,i=1, tells you where to start and
the upper index, 5, tells you where to end. You should practice reading and understanding sigma notation because it
is used heavily in Calculus.
Example A
Write out all the terms of the series.
8
k∑= 42 k
Solution:
8
k∑= 42 k=^2 ·^4 +^2 ·^5 +^2 ·^6 +^2 ·^7 +^2 ·^8