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Evaluating Summation Notation (Sigma)
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:
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On the Calculator: |
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Example 2: Evaluate 
Notice that the starting value is negative. |
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Investigate! What happens when the top value is one less than the bottom value?
Evaluate 
If the top value is one less than the bottom value, the answer is always 0. |
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What happens when the top value is more than one less than the bottom value?
Evaluate 
This equals 
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.
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and choose the sigma notation. 
