Summation Notation

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# Summation Notation - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Summation Notation' - russ

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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

ak is the formula used to generate each term of the sum

k is called the index of summation

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

Summation Notation
• Properties

(i)

(ii)

Note: Not true

Summation Notation
• Properties (cont)

(iii) for

(iv)

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

Round answers to 12 decimal places.

• Soln. 0.999999999713