12.5 Sigma Notation.notebook
May 22, 2012
Unit 12, Sequences and Series
12.5 Sigma Notation and the nth term
NCSCOS 2.07, "Use recursively defined
functions to model and solve problems."
WIMD: What I must do:
I will use Sigma, Σ, notation to write series expressions and equations
Key words:
sigma notation
index of summation
REVIEW and REFERENCE
For arithmetic series:
For geometric series:
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12.5 Sigma Notation.notebook
May 22, 2012
12.5 Sigma Notation and the nth term
The Greek letter sigma indicates a sum or series.
max value of n
expression for the general term
starting value where k is an integer value, and n and k represent the starting and ending terms in the sequence
Ex. 1 Write each expression in expanded form then find the sum.
Method 1: Expand by hand
1 Answer?
3244
2
12.5 Sigma Notation.notebook
May 22, 2012
Ex. 1 Write each expression in expanded form then find the sum.
Ref: p795
Method 2: use the calculator to find the sum of a series.
press
2nd ⇒ STAT ⇒ MATH ⇒ sum(
then do,
2nd ⇒ STAT ⇒ OPS ⇒ seq(
next type:
function , x, initial n, final n, 1
Ex. 2 Write in expanded form then find the sum of the infinite series
2 Answer?
3
3
12.5 Sigma Notation.notebook
May 22, 2012
Helpful Hints for writing Sigma Notation for a series
If it looks like each term is being added by the same number then this mean to multiply that number (being added) by the variable:
ex. 5 + 8 + 11 + ...
terms are increasing
by 3 each time
If it looks like each term is being multiplied by the same number then this means to raise that number (the multiplier) to the power of n ex. ­4 ­ 8 ­ 16 ­ 32 ­ 64
terms are being multiplied by 2
each time
If the series has alternating signs from positive to negative values (oscillating) then we need to include a sign changing value of (­1)n: ex. ­3 + 9 ­ 27 + 81
sign changing value
If part of a series is increasing very rapidly, but not by a common ratio, then we may need to use a factorial.
increases values ex. quickly, but not by a constant #
Express each series below using sigma notation
* notice the series is finite 4
12.5 Sigma Notation.notebook
May 22, 2012
Express using sigma notation
Recall that, A factorial is denoted by the symbol n! example: 4! = (4)(3)(2)(1) = 24
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12.5 Sigma Notation.notebook
May 22, 2012
Ex. 3 Express each series below using sigma notation
a.
* notice the series is finite
Practice: Express the series below using sigma notation
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12.5 Sigma Notation.notebook
May 22, 2012
Practice: Express the series below using sigma notation
Access Code: E7BE47BB9B
Glencoe Quizzes
Homework
p798, #23­45
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12.5 Sigma Notation.notebook
May 22, 2012
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12.5 Sigma Notation.notebook
May 22, 2012
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Attachments
Glencoe Pre­Calc on line quizzes
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