Series
Seriesand
andSummation
SummationNotation
Notation
• How do we find the terms of an
arithmetic sequence?
• How do we find the sum of an
arithmetic series?
HoltMcDougal
Algebra 2Algebra 2
Holt
Series and Summation Notation
Finding the sum of a series with many terms can be
tedious. You can derive formulas for the sums of some
common series.
In a constant series, such as 3 + 3 + 3 + 3 + 3, each term
has the same value.
The formula for the sum of a constant series is
as shown.
Holt McDougal Algebra 2
Series and Summation Notation
A linear series is a counting series, such as the sum
of the first 10 natural numbers.
Examine when the terms are rearranged.
Holt McDougal Algebra 2
Series and Summation Notation
Notice that 5 is half of the number of terms and
11 represents the sum of the first and the last
term, 1 + 10. This suggests that the sum of a
linear series is
, which can be written
as
Similar methods will help you find the sum of a
quadratic series.
Holt McDougal Algebra 2
Series and Summation Notation
Holt McDougal Algebra 2
Series and Summation Notation
Caution
When counting the number of
terms, you must include both the
first and the last. For example,
has six terms, not five.
k = 5, 6, 7, 8, 9, 10
Holt McDougal Algebra 2
Series and Summation Notation
Using Summation Formulas
Evaluate the series.
1.
Constant series
Method 1 Use the
summation formula.
There are 7 terms.
Holt McDougal Algebra 2
Method 2 Expand and
evaluate.
Series and Summation Notation
Using Summation Formulas
Evaluate the series.
2.
Linear series
Method 1 Use the
summation formula.
Holt McDougal Algebra 2
Method 2 Expand and
evaluate.
Series and Summation Notation
Using Summation Formulas
Evaluate the series.
3.
Quadratic series
Method 1 Use the
summation formula.
n(n + 1)(2n + 1)
=
6
= 12(12 + 1)(2 · 12 + 1)
6
(156)(25)
=
6
= 650
Holt McDougal Algebra 2
Method 2 Use a
calculator.
Series and Summation Notation
Using Summation Formulas
Evaluate the series.
4.
Constant series
Method 1 Use the
summation formula.
There are 60 terms.
= nc = 60(4) = 240
Method 2 Expand and
evaluate.
=4+4+4+4+4
+4+4+...+4
60 items
= 240
Holt McDougal Algebra 2
Series and Summation Notation
Using Summation Formulas
Evaluate the series.
5.
Linear series
Method 1 Use the
summation formula.
Method 2 Expand and
evaluate.
=1+2+3+4+5
+6+7+8+9+
10 + 11 + 12 + 13
+ 14 + 15 = 120
Holt McDougal Algebra 2
Series and Summation Notation
Using Summation Formulas
Evaluate the series.
6.
Quadratic series
Method 1 Use the
summation formula.
n(n + 1)(2n + 1)
=
6
= 10(10 + 1)(2 · 10 + 1)
6
(110)(21)
=
6
= 385
Holt McDougal Algebra 2
Method 2 Use a
calculator.
Series and Summation Notation
Lesson 5.2 Practice B
Holt McDougal Algebra 2