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Summation Notation

Summation Notation. Terminology. The Greek letter, , indicates a sum and is referred to as a summation operation. k is referred to as the index of summation (or summation variable). a k is referred to as the k -th term of the sum

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Summation Notation

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  1. Summation Notation

  2. Terminology The Greek letter, , indicates a sum and is referred to as a summation operation. 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

  3. Example - Evaluate Here The upper and lower limits are 1 and 4

  4. 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

  5. Why Use Summation Notation Summation notation allows use to write expression compactly. For example suppose that there are n pair-wise mutually exclusive events E1, E2, …, En. Then we may write

  6. Properties for Summation 1. 2. 3.

  7. Properties (continued) 4. 5. 6.

  8. Exercises Calculate the sums indicated below: • . • . • .

  9. More Exercises Write the sum using summation notation • . • .

  10. Still More Exercises Find the sum • . • .

  11. The Last of the Exercises • Re-index the sum in Exercise 2 to run from 0 to 2 • Re-index the sum in Exercise 3 to run from 1 to 5

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