1. Summation Notation

2.  Shorthand way of expressing a sum  Uses the Greek letter sigma: ∑ k is called the index of summation n is called the upper limit of the summation a k is the formula used to generate each term of the sum

3. Summation Notation  Any letter can be used to index a summation

4. Summation Notation  Ex: Evaluate the following sum:  Sol:

5. Summation Notation  Ex: Evaluate the following sum:  Sol:

6. Summation Notation  Recall from Basic Probability, that for any two events E and F:  If E and F are mutually exclusive, then P(E ∩ F) = 0, which means:

7. Summation Notation  The last statement can be generalized for several events  For events no two of which can take place at the same time, then Summation notation is so much easier to write

8. Summation Notation  Properties (i) (ii) Note: Not true

9. Summation Notation  Properties (cont) (iii) for (iv)

10. Summation Notation  Ex: Evaluate the following sum using (i) direct computation and (ii) Excel  Sol: Direct computation

11. Summation Notation  Using Excel

12. Summation Notation  Use Excel to evaluate. Round answers to 12 decimal places.  Soln. 0.999999999713