This preview shows page 1. Sign up to view the full content.
Unformatted text preview: (a) lim n 1 n 3 (b) lim n 3 n 21 n + 1 (c) lim n 3 n 2 + sin( n ) n 2 (d) lim n 5 n 42 n 2 + n + 1 n 2 ( n 2 + 1) 4. Let ( s n ) n =1 and ( t n ) n =1 be sequences. Decide which of the following statements are true. In each case, provide a proof or a counterexample. (a) If ( s n ) n =1 and ( t n ) n =1 are both divergent then so is ( s n + t n ) n =1 . (b) If ( s n ) n =1 and ( t n ) n =1 are both divergent then so is ( s n t n ) n =1 . (c) If ( s n ) n =1 and ( s n + t n ) n =1 are both divergent then so is ( t n ) n =1 . (d) If ( s n ) n =1 is convergent then so is (1 /s n ) n =1 . 1...
View
Full
Document
 Winter '11
 Wiley
 Differential Equations, Calculus, Equations

Click to edit the document details