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 a n = c exists we have that c = c + 90 10 or c = 10. Thus we expect that the sequence increases towards 10. a) The sequence is bounded above by 10. To see this we use induction. It is true or a 1 since a 1 = 5 < 10. Assume it is true or some n , i.e., a n 10. Then a n +1 10 + 90 10 = 10 1 which proves what we have claimed. b) Next we check that a n is increasing. Calculate a n +1a n = a n + 90 10a n = 9 10a n 10 since a n 10. c) c = 10. d) Next, note that 10a n +1 = 10a n + 90 10 = 10a n 10 = 1 10 (10a n ) . Thus 10a n +1 = 1 10 n (10a 1 ) = 5 1 10 n . Thus if n = 7 we get that 5107 < 106 and hence a n < 106 for all n 8. 2...
View
Full
Document
 Fall '08
 N/A
 Calculus

Click to edit the document details