Summation Notation

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Summation Notation
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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

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Summation Notation

• Ex Evaluate the following sum
• Sol

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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 n 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

• Using Excel

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Summation Notation

• Use Excel to evaluate .
• Round answers to 12 decimal places.
• Soln. 0.999999999713