2. Find the sum of , if it exists.
Needs to be between -1<r<1
Find the sum of , if it exists.
First, find the value of r to determine if the sum exists.
the sum does not exist.
Answer: The sum does not exist.
Example 5-1a

3. Find the sum of , if it exists.
the sum exists.
Example 5-1a

4. Now use the formula for the sum of an infinite geometric series.
Sum formula
Simplify.
Answer: The sum of the series is 2.
Example 5-1a

5. Find the sum of each infinite geometric series, if it exists. a.b.
Answer: no sum
Answer: 2
Example 5-1b

6. In this infinite geometric series,
Evaluate
In this infinite geometric series,
Sum formula
Simplify.
Example 5-2a

7. Answer: Thus,
Example 5-2a

8. Evaluate
n = 1
Answer: 3
Example 5-2b

9. Write the repeating decimal as a sum.
Write as a fraction.
Method 1
Write the repeating decimal as a sum.
Example 5-3a

10. In this series,
Sum formula