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Summation Notation

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

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Summation Notation

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  1. Summation Notation

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

  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

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