Lecture notes Business mathematics (BMD115D)

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CHAPTER 8

SIGMA NOTATION

AIM: To introduce the sigma notation
To rewrite sums in terms of sigma notation
To sum elements through using sigma notation

8.1 INTRODUCTION

PQPO OQQ«O OPPP ««QOPQ
QO« « PPQOP QO« «««Q
« OP «

I have 4 boxes filled with pencils.
How many pencils do I have in each box?

11 10 8 10

How many pencils do I have in all?

11 + 10 + 8 + 10

= 39 pencils.
This Greek capital letter sigma ( ) , for the purpose of this course, means ‘add together the
appropriate values’.

If we want to add 4 values of a variable ( let’s say the name of the variable is X ) , we can express
the sum as follows :

X1 + X2 + X3 + X4

There is a much shorter notation to write the sum, called the sigma notation :




The above notation implies that you must sum all the X - values, starting at the first X value up
to the 4th X value. The letter ‘i’ is an index value and shows the position of the variable that has
to be added.

To indicate we are going to sum a list of values, we use the sigma - notation.

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EXAMPLE 8.1

8.1.1 X1 + X2 + X3 = 8.1.2 X3 + X4 + X5 =


8.1.3 Y1 + Y2 + Y3 + Y4 = 8.1.4 Y5 + Y6 + Y7 + Y8 + Y9 =

EXERCISE 8.1

Let X be a variable that can take on the following values :

3; 5; 6; 8; 7; 5; 4
Calculate :




8.2 SUMMATION OVER TWO VARIABLES

In the previous paragraph we have looked at the sigma notation when we added one variable only.
It is, however, possible to add two variables at the same time and still use the sigma notation.

There are two very important rules that you have to remember:

RULE 1




RULE 2