This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: n 2 n +1 + 3 n +1 ; (c) a n = p n 2 + np n 2n ; (d) a n = 1 1 2 + 1 2 3 + + 1 n ( n + 1) . 2 8. Prove the following equalities (a) lim n 2 n n ! = 0; (b) lim n n k a n = 0 ( a > 1); (c) lim n a n n ! = 0; (d) lim n nq n = 0 , if  q  < 1; (e) lim n n a = 1; (f) lim n n n = 1; (g) lim n 1 n n ! = 0 . 9. Let ( a n ) n N + be a convergent sequence of positive numbers. Prove that lim n n a 1 a 2 ...a n = lim n a n . 10. Let ( a n ) n N + be a sequence of positive numbers such that the limit lim n a n a n1 exists. Prove that lim n n a n = lim n a n a n1 ....
View
Full
Document
This note was uploaded on 02/25/2010 for the course MATHEMATIC 11007 taught by Professor Spyros during the Winter '10 term at Bristol Community College.
 Winter '10
 Spyros

Click to edit the document details