quiz6ans - does it converge absolutely? n =0 3 n x n ( n...

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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
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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...
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