1. Ratio Test & Root Test
Lesson 9.6

2. Ratio Test For a series of positive terms
We realize that for convergence to happen the sequence { ak } must be "rapidly" decreasing towards zero
Consider the limit of the ratio
Ratio test says:
If L < 1 then converges
If L > 1 or L is infinite, then diverges
If L = 1, the test is inconclusive

3. Works Best … The ratio test works best in such series as
Note that k appears as an exponent or a factorial

4. Use It or Lose It Use the ratio test for the following series
Convergent or divergent?

5. The Root Test Easiest test we've seen was the divergence test
Look at
If so, the series diverges
However does not guarantee convergence

6. The Root Test Possible to look at Try this out with
If L < 1, then converges
If L > 1 or if L is infinite then diverges
If L = 1, the root test is inconclusive
Try this out with

7. Assignment
Lesson 9.6
Page 645
Exercises 5 – 49 EOO