Ratio Test & Root Test Lesson 9.6

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

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

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

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

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

Assignment Lesson 9.6 Page 645 Exercises 5 – 49 EOO