This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Homework 3 - Math 139
Due Sep 22nd Instructor
Web page Mauro Maggioni
293 Physics Bldg.
www.math.duke.edu/˜ mauro/teaching.html Reading: from Reed’s textbook: Sections 2.4,2.5
§1.3: #3(c) , 8. In both exercises, note that the sets need not be disjoint!
Additional Problem: Show that limn→+∞ r n does not exist if r ≤ −1, by showing that
for any L ∈ R, the statement
lim r n = L
n→∞ is false. [Suggested steps: after carefully stating what you want to prove, take ǫ = 1 in
your statement. If |L − r n | > 4 (what is n?), you are good. If not, notice that |r n − r n+1 | ≥
1 (why?), then use the inequality of #10, §1.1 to conclude that |L − r n+1 | > 1/4). ...
View Full Document
- Fall '08