Summation Notation

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Summation Notation
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The Greek letter, ?, indicates a sum and is
referred to as a summation operator. k is
referred to as the index of summation (or
summation variable). ak is referred to as the
k-th term of the sum The numbers 1 and n are the
lower and upper limits of the summation,
respectively
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Evaluate

• Here
• The upper and lower limits are 1 and 4

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Basic Ideas

• As with functions, the letter used to denote the
  index of summation is immaterial
• The index of summation need not start at 1

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Why Use Summation Notation

• Summation notation allows us to write expression
  compactly. For example suppose that there are n
  pair-wise mutually exclusive events E1, E2, ,
  En. Then we may write

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Properties for Summation
1. 2. 3.
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Properties (continued)
4. 5. 6.
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Exercises

• Calculate the sums indicated below
• .
• .
• .

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More Exercises

• Write the sum using summation notation
• .
• .

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Still More Exercises

• Find the sum
• .
• .

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The Last of the Exercises

• Re-index the sum in Exercise 2 to run from 2 to 6
• Re-index the sum in Exercise 3 to run from 0 to 7