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Evaluating Summation Notation

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).  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:

sigma=
sum

On the Calculator:
 

Example 1: Evaluate

Use the template to bring up the summation notation (sigma).

Press control keytemplate and choose the sigma notation. ENTER.

sigma1
Use the TAB key to move through the template entering your values.
sigma2


Example 2: Evaluate sum 15

Notice that the starting value is negative.

sigma3


Investigate! What happens when the top value is one less than the bottom value?

Evaluate sigma question

If the top value is one less than the bottom value, the answer is always 0.

sig4

What happens when the top value is more than one less than the bottom value?

Evaluate sig qht

This equals ss

To get this new equivalent summation, add one to the top value and move it to the bottom. Subtract one from the bottom value and move it to the top. Negate this entire new sum.

 

 

sig5

investigate pic

 

 



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