1 or L is infinite, then diverges If L = 1, the test is inconclusive"> 1 or L is infinite, then diverges If L = 1, the test is inconclusive">

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Ratio Test & Root Test Lesson 9.6.

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Presentation on theme: "Ratio Test & Root Test Lesson 9.6."— Presentation transcript:

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


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