Holt McDougal Algebra 2

Series and Summation NotationSeries and Summation Notation

Holt Algebra 2Holt McDougal Algebra 2

• How do we find the terms of an arithmetic sequence?

• How do we find the sum of an arithmetic series?

Holt McDougal Algebra 2

Series and Summation NotationFinding 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

Similar methods will help you find the sum of a quadratic series.

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

Holt McDougal Algebra 2

Series and Summation Notation

Holt McDougal Algebra 2

Series and Summation Notation

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

Caution

Holt McDougal Algebra 2

Series and Summation Notation

Evaluate the series.Using Summation Formulas

Method 1 Use the summation formula.There are 7 terms.

Method 2 Expand and evaluate.

Constant series1.

Holt McDougal Algebra 2

Series and Summation Notation

Evaluate the series.Using Summation Formulas

Method 1 Use the summation formula.

Method 2 Expand and evaluate.

Linear series2.

Holt McDougal Algebra 2

Series and Summation Notation

Evaluate the series.Using Summation Formulas

Method 1 Use the summation formula.

Method 2 Use a calculator.

Quadratic series3.

= 650

n(n + 1)(2n + 1) 6=12(12 + 1)(2 · 12 + 1) 6=(156)(25) 6=

Holt McDougal Algebra 2

Series and Summation Notation

Evaluate the series.Using Summation Formulas

Method 1 Use the summation formula.

Constant series

There are 60 terms.= nc = 60(4) = 240

4.

Method 2 Expand and evaluate.

= 240

= 4 + 4 + 4 + 4 + 4 + 4 + 4 + . . . + 4

60 items

Holt McDougal Algebra 2

Series and Summation Notation

Evaluate the series.Using Summation Formulas

Linear series5.

Method 1 Use the summation formula.

= 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 = 120

Method 2 Expand and evaluate.

Holt McDougal Algebra 2

Series and Summation Notation

Evaluate the series.Using Summation Formulas

= 385

Quadratic series 6.

Method 1 Use the summation formula.

Method 2 Use a calculator.

n(n + 1)(2n + 1) 6=10(10 + 1)(2 · 10 + 1) 6=(110)(21) 6=

Holt McDougal Algebra 2

Series and Summation Notation

Lesson 5.2 Practice B