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 absolutely on1 3 < x < 1 3 . If you check both endpoints, you should get that they also converge absolutely. Thus, it converges absolutely on1 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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 Fall '08
 Wilson
 Math, Calculus, Mathematical Series, following questions, Stephen Hawking, 1 pt, A Brief History of Time, series converge

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