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Evaluating Summation (Sigma) Notation
(Function Mode)
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A shorthand notation is used to represent sums with more than a few
terms.
This shorthand notation uses the Greek letter sigma (which denotes sum).
(The entries below and above the symbol are referred to as the index values.)
See Sigma Notation and Series if you need a refresher on working with sigma.
If we have a rule, such as f (n), which assigns the value f (n) to each integer n in the set of integers
{ j, j+1, j+2, ... k }, we can represent the sum as:
 = 
On the Graphing Calclator
Let's start with the easiest way to enter sigma on the calculator,
then look at other methods further down the page.
 Function Short Cut Menu
 :
Hit alpha key, followed by window key.
Choose option 2. summation
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In MathPrint mode, a template appears
for entering a sigma notation.
In Classic mode, a sigma appears
waiting for an entry of the form
(expression, variable, starting index, ending index)
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Example 1: Evaluate: 
notice that this sum starts
with k = 2
In MathPrint mode:
alpha, window, #2 summation,
fill in template
* You can replace "k" with any letter you want, including "x". |
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Example 2: Evaluate: notice that this sum starts
with r = -1
In Classic mode:
We are using "x" to replace "r"
as it is easier to access "x".
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Alternative steps to access sigma:
Use MATH key and slide down (or back up) to option 0: summation.
Methods of Finding Summation without Using Sigma:
following format for "classic mode"
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The sum feature and the seq feature can also be used when working with
summations.
On the
calculator, a summation can be interpreted as follows:
The right hand side of the statement above can be used to find a summation wthout envoking sigma.
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2nd STAT (LIST) → MATH
#5 sum
The format for sum is sum( list )
where list will be the terms of
the rule
 .
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2nd STAT (LIST) →
OPS Choose #5 seq(
The format for seq: expression,
variable,
starting value, ending value, increment.
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While sequences have a domain of
natural numbers, {1, 2, 3, 4, ...}, in Func mode, the sequence command will
accept integer domain values less than one. (In Seq mode, however, the sequence command will accept only
integer domain values of 1 or greater.)
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(For ease of entry, x was used as the variable in both examples above.
If you wish to use the designated variable, type it into the
calculator using the alpha
key.)
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If
you think you are going to forget these commands:
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Another approach to Example 1:
Type the number of terms needed into L1.
Type the rule into L2.
Add the answers manually on the HOME screen.
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Or, have the calculator do the
adding. If you do not want to add manually on the home
screen, you can use the cumulative
summation feature (cumSum) to add L2.
Remember that Example 1 starts with k = 2.
To find cumSum(
, go to LIST
(2nd STAT),
arrow to OPS
heading, and choose #6 cumSum(. |
Enter cumSum(L2) as
the
pattern to determine L3. |
The entry in column L3
corresponding to the value 7
in L1 will be the
sum. |
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Finding Your Way Around TABLE of
CONTENTS
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