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). a k 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 E 1, E 2, …, E n. Then we may write

6. Properties for Summation 1. 2. 3.

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

8. Exercises Calculate the sums indicated below: 1.. 2.. 3..

9. More Exercises Write the sum using summation notation 4.. 5..

10. Still More Exercises Find the sum 6.. 7..

11. The Last of the Exercises 8.Re-index the sum in Exercise 2 to run from 0 to 2 9.Re-index the sum in Exercise 3 to run from 1 to 5