1. Warm Up
Use summation notation to write the series for the specified number of terms.
…; n = 7

2. Answer
Use summation notation to write the series for the specified number of terms.
…; n = 7

3. Convergent and Divergent Series

4. What will happen to the terms of this sequence as it continues forever?
It approaches 0!

5. Convergent Sequence
A sequence is converging if its terms approach 0. *Only applies to geometric sequences.

6. Determine if the following sequences are convergent or divergent:

7. Sum of an Infinite Geometric Series
We can find the sum of this series, even though it goes on forever, because it is convergent.

8. Sum of an Infinite Geometric Series
The following conditions must be true to use this formula:
The series must be geometric
The series must be convergent
The series must be infinite

9. Example 1
Determine whether each infinite geometric series diverges or converges. If it converges, find the sum.
a) …
b) …

10. Example 2
Evaluate each infinite geometric series a) b)

11. Formula Recap
Sequence
Series
Arithmetic
Geometric
Finite
Infinite