Unformatted text preview: counterexample. (a) If the sequence of partial sums of a series is bounded then the series converges. (b) If ∑ a n converges then ∑ (1) n a n converges. (c) Suppose ∑ ∞ n =0 a n , ∑ ∞ n =0 b n and ∑ ∞ n =0 a n b n converge. Then ( ∑ ∞ n =0 a n )( ∑ ∞ n =0 b n ) = ∑ ∞ n =0 a n b n (d) If  a n  ≥  b n  for all n and ∑ b n diverges then ∑ a n diverges. 1...
View
Full
Document
This note was uploaded on 10/18/2011 for the course MATH V1102 taught by Professor Mosina during the Fall '08 term at Columbia.
 Fall '08
 Mosina
 Calculus

Click to edit the document details