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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 notation2
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

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Summation Notation
  • Any letter can be used to index a summation
summation notation4
Summation Notation
  • Ex: Evaluate the following sum:
  • Sol:
summation notation5
Summation Notation
  • Ex: Evaluate the following sum:
  • Sol:
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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:
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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

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Summation Notation
  • Properties

(i)

(ii)

Note: Not true

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Summation Notation
  • Properties (cont)

(iii) for

(iv)

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Summation Notation
  • Ex: Evaluate the following sum using (i) direct computation and (ii) Excel
  • Sol: Direct computation
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Summation Notation
  • Use Excel to evaluate .

Round answers to 12 decimal places.

  • Soln. 0.999999999713