Alg2 Notes 9.2.notebook
April 10, 2013
9­2 Series and Summation Notation Find the first five terms of the sequence.
1.
2.
Write a possible explicit and recursive rule for the nth term of each sequence.
3. 1, 2, 4, 8, 16, ...
4. 4, 7, 10, 13, 16, ...
Warm­up Answers
Find the first five terms of the sequence.
1.
2.
5, 11, 23, 47, 95, 191
1 2 3 4 5
2 3 4 5 6
Write a possible explicit and recursive rule for the nth term of each sequence.
3. 1, 2, 4, 8, 16, ...
4. 4, 7, 10, 13, 16, ...
Recursive
Explicit
Explicit Recursive
Alg2 Notes 9.2.notebook
April 10, 2013
9­2 Series and Summation Notation Evaluate the sum of a series.
Evaluate the sum of a series in sigma notation.
Write each series in summation notation.
Adding Areas in Calculus
I. Summation Notation Sums
A series can also be represented by using summation notation, which uses the Greek letter Σ (capital sigma) to denote the sum of a sequence defined by a rule, as shown.
Alg2 Notes 9.2.notebook
April 10, 2013
II. Expanding Sums Because many sequences are infinite and do not have defined sums, we often find partial sums. A partial sum, indicated by Sn, is the sum of a specified number of terms of a sequence.
1. Evaluate 2. Evaluate
3. Evaluate 4. Evaluate
Alg2 Notes 9.2.notebook
April 10, 2013
III. Writing Sums in Summation Notation
5. Write the series in summation notation.
Step 1 Find a rule for the kth term of the sequence.
ak = 4k
Step 2 Write the notation for the first 5 terms
4 + 8 + 12 + 16 + 20
6. Write the series in summation notation.
Step 1 Find a rule for the kth term of the sequence.
Step 2 Write the notation for the first 5 terms
Note, for sequences with alternate signs:
Alg2 Notes 9.2.notebook
April 10, 2013
7. Write the series in summation notation.
Step 1 Find a rule for the kth term of the sequence.
Step 2 Write the notation for the first 5 terms
IV. Using Summation Formulas
What about obnoxious ones like these?
Alg2 Notes 9.2.notebook
April 10, 2013
8. Evaluate each series.
V. Application
9. Sam is laying out patio stones in a triangular pattern. The first row has 2 stones and each row has 2 additional stones, as shown below. How many complete rows can he make with a box of 144 stones?
Alg2 Notes 9.2.notebook
April 10, 2013
9.2 p.638 #2 ­ 12 all, 14, 17 ­ 33 odd, 50, 57, 61
In­Class:
Challenge Worksheet A, B, C, and D