Study Guides (238,613)
Mathematics (538)
MAT136H1 (46)
all (27)
Midterm

# 11.6 Absolute Convergence & Ratio and Root Tests Question #3 (Medium)

1 Page
127 Views

School
University of Toronto St. George
Department
Mathematics
Course
MAT136H1
Professor
all
Semester
Winter

Description
11.6 Infinite Sequences & Series Absolute Convergence & Ratio and Root Tests Question #3 (Medium): Alternating Series Tested Using the Ratio Test Strategy The ratio test states: 1) | | means ∑ is absolutely convergent (ie. convergent) 2) | | , or means ∑ is divergent 3) | | means no conclusion can be drawn from the Ratio Test about convergence or divergence of ∑ Notice that the ratio is inside the absolute value sign. Therefore, even alternating series can be tested for its convergence or divergence using this ratio test. Sample Question Determine if the series is absolutely convergent, conditionally convergent, or divergent. ∑ ( ) ( ) Solution The given series is an alternating series, however it can still be tested against the ratio test to see any conclusion can be drawn about its convergence, divergence. Since the ratio is placed inside the absolute value sign for the ratio test, the alternating sign
More Less

Related notes for MAT136H1

OR

Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.