quiz6ans - does it converge absolutely ∑ ∞ n =0 3 n x n...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 222, Quiz 6 Name: Circle One: 11:00 12:05 Instructions: Answer the following questions fully, and circle your an- swer. 1) Determine whether the series is absolutely convergent, conditionally convergent, or divergent. n =1 ( - 1) n n ( n +1) Use the alternating series test. This shows it converges. Take the abso- lute value, and do a limit comparison to 1 n to show that it does not converge absolutely, thus it converges conditionally. 2) Find the radius of convergence for the following power series. For what values of x does the series converge conditionally, and for what values
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: does it converge absolutely? ∑ ∞ n =0 3 n x n ( n +1) 2 Use the ratio test to show the the radius is 1 3 . Thus, it converges abso-lutely on-1 3 < x < 1 3 . If you check both endpoints, you should get that they also converge absolutely. Thus, it converges absolutely on-1 3 ≤ x ≤ 1 3 and converges conditionally nowhere. Bonus (1 pt): Who is the author of “A Brief History of Time”? (Hint: He has appeared in three Simpsons episodes and one episode of Futurama) Stephen Hawking. I highly recommend the book. 1...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern