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Unformatted text preview: lim n (  (1) n (8 1 /n 21) n  ) 1 /n = lim n 8 1 /n 21 = 0 . Since 0 < 1, the root test applies, and we can conclude that the series converges absolutely. 3. (2 points) (a) Find an x such that the power series n =1 n ! x n converges. Solution: x = 0. (b) Find an x such that the power series n =1 ( 1 2 ) n x n diverges. For any x with  x  > 2, the terms ( x/ 2) n diverge, so the power series diverges. 1...
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This note was uploaded on 03/25/2011 for the course MATH 1B taught by Professor Reshetiken during the Fall '08 term at University of California, Berkeley.
 Fall '08
 Reshetiken
 Math

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