Appendix ESigma Notation

AP CalculusNovember 11, 2009Berkley High School, D1B1todd1@toddfadoir.com

Calculus, Appendix E, Todd Fadoir, CASA, 2003 2

Sigma Notation

Sigma Notation gives us a shorthand for writing series.

5

1

1 2 3 4 5 15i

i

Calculus, Appendix E, Todd Fadoir, CASA, 2003 3

Interpreting Sigma Notation

5

1i

i

Iterative variable

Starting value

Ending value

“To sum” orsummation

Some expression

Sum the value of i as i ranges from 1 to 5

Calculus, Appendix E, Todd Fadoir, CASA, 2003 4

Interpreting Sigma Notation

seq() is 2nd List:Ops:5 sum() is 2nd List:Math:5

5

1

15i

i

Iterative variable

Starting value

Ending value

“To sum” orsummation

Some expression

Calculus, Appendix E, Todd Fadoir, CASA, 2003 5

Example

seq() is 2nd List:Ops:5 sum() is 2nd List:Math:5

52

1

2 2 2 2 21 2 3 4 5 55

i

i

Calculus, Appendix E, Todd Fadoir, CASA, 2003 6

Example: Without Calculators5

2

1

2 2 2 2 2

52

1

1 2 3 4 5 55

5(5 1)(2 5 1)

6

5(6)(11)

655

i

i

i

i

1

1

2

1

23

1

It is easy to add these numbers,

but it has been proven that...

( 1)

2

( 1)(2 1)

6

( 1)

2

n

i

n

i

n

i

n

i

c cn

n ni

n n ni

n ni

Calculus, Appendix E, Todd Fadoir, CASA, 2003 7

Examples

Name the series that matches the sigma notations…

10

8

8

6

8

6

8 9 10

(2 ) 12 14 16

(2 1) 13 15 17

i

i

i

i

i

i

Calculus, Appendix E, Todd Fadoir, CASA, 2003 8

Examples

Name the sigma notations that matches the series …

101

8

42

2

41 1 12 3 4

2

8 9 10 ( ( 1 ))

4 9 16 ( )

1

i

i

i

i

i

i

i

Calculus, Appendix E, Todd Fadoir, CASA, 2003 9

Examples

Name the sigma notations that matches the series …

1

1 1 12 3

1

1

1 2 3 ...

11 ...

2 4 6 ... 2 (2 )

n

i

n

ni

n

i

n i

i

n i

Calculus, Appendix E, Todd Fadoir, CASA, 2003 10

Assignment

Appendix E, 1-36, all