1. Copyright © 2007 Pearson Education, Inc. Slide 11-1 11-5 Geometric Series A geometric series is the sum of the terms of a geometric sequence. Sum of the First n Terms of a Geometric Sequence If a geometric sequence has first term a 1 and common ratio r, then the sum of the first n terms is given by where.

2. Copyright © 2007 Pearson Education, Inc. Slide 11-2 Evaluate the series to the given term.

3. Copyright © 2007 Pearson Education, Inc. Slide 11-3 Evaluate the series to the given term.

4. Copyright © 2007 Pearson Education, Inc. Slide 11-4 11-5 Infinite Geometric Series Sum of the Terms of an Infinite Geometric Sequence The sum of the terms of an infinite geometric sequence with first term a 1 and common ratio r, where –1 < r < 1 is given by meaning it converges. If r > 1 or r < -1 then it does not converge. We call this diverge.

5. Copyright © 2007 Pearson Education, Inc. Slide 11-5 Decide whether each infinite geometric series converges or diverges then state whether it’ll have a sum. 3. 72 + 36 + 18 + 9 + … 4. 27 + 9 + 3 + 1 +… 5. 13 + 26 + 52 + …

6. Copyright © 2007 Pearson Education, Inc. Slide 11-6 Summation Notation for infinite geometric series

7. Copyright © 2007 Pearson Education, Inc. Slide 11-7 Evaluate each infinite series that has a sum

8. Copyright © 2007 Pearson Education, Inc. Slide 11-8 Evaluate each infinite series that has a sum

9. Copyright © 2007 Pearson Education, Inc. Slide 11-9 Evaluate each infinite series that has a sum

10. Copyright © 2007 Pearson Education, Inc. Slide 11-10 Suppose your business made a profit of $4000 the first year. If the profit increases 25% per year, find the total profit over the first 6 years.