This preview shows page 1. Sign up to view the full content.
Unformatted text preview: lim n ( | (-1) n (8 1 /n 2-1) n | ) 1 /n = lim n 8 1 /n 2-1 = 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...
View Full Document
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