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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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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
Example - Evaluate Here The upper and lower limits are 1 and 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
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
Properties for Summation 1. 2. 3.
Properties (continued) 4. 5. 6.
Exercises Calculate the sums indicated below: • . • . • .
More Exercises Write the sum using summation notation • . • .
Still More Exercises Find the sum • . • .
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