Seriesand and Summation Notation How do we find

Seriesand and. Summation. Notation • How do we find the terms of an arithmetic sequence? • How do we find the sum of an arithmetic series? Holt. Mc. Dougal Algebra 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, each term has the same value. The formula for the sum of a constant series is as shown. Holt Mc. Dougal 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 Mc. Dougal Algebra 2

Series and Summation 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 Mc. Dougal Algebra 2

Series and Summation Notation Holt Mc. Dougal 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 Mc. Dougal 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 Mc. Dougal Algebra 2 Method 2 Expand evaluate.

Series and Summation Notation Using Summation Formulas Evaluate the series. 2. Linear series Method 1 Use the summation formula. Holt Mc. Dougal Algebra 2 Method 2 Expand evaluate.

Series and Summation Notation Using Summation Formulas Evaluate the series. 3. Quadratic series Method 1 Use the summation formula. n(n + 1)(2 n + 1) = 6 = 12(12 + 1)(2 · 12 + 1) 6 (156)(25) = 650 Holt Mc. Dougal 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 evaluate. =4+4+4+. . . +4 60 items = 240 Holt Mc. Dougal Algebra 2

Series and Summation Notation Using Summation Formulas Evaluate the series. 5. Linear series Method 1 Use the summation formula. Method 2 Expand evaluate. =1+2+3+4+5 +6+7+8+9+ 10 + 11 + 12 + 13 + 14 + 15 = 120 Holt Mc. Dougal Algebra 2

Series and Summation Notation Using Summation Formulas Evaluate the series. 6. Quadratic series Method 1 Use the summation formula. n(n + 1)(2 n + 1) = 6 = 10(10 + 1)(2 · 10 + 1) 6 (110)(21) = 6 = 385 Holt Mc. Dougal Algebra 2 Method 2 Use a calculator.

Series and Summation Notation Lesson 5. 2 Practice B Holt Mc. Dougal Algebra 2