1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

2 in 1

  1. Aug 15, 2008 #1
    1. The problem statement, all variables and given/known data

    Hey guys, can you help me with this on please?
    First one, I need to proof convergence, and the second one is to find the radius of converge.

    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

    • 1.jpg
      1.jpg
      File size:
      14.8 KB
      Views:
      48
  2. jcsd
  3. Aug 15, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    For the first one, you are given the first series converges. That means a_n->infinity. Think comparison test. 1/(a_n-x)<1/(a_n-y) if x<y<a_n. How about choosing y=a_n/2?? Can you justify that? For the second one, write it as [(n+1)^n/n^n]*[1/n^z]. The first factor has a limit. What is it?
     
  4. Aug 15, 2008 #3
    Right, it's e. so that's mean that in order for the series to converge, x need to bigger then 1?
     
  5. Aug 15, 2008 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Looks to me like aside from the e, it's a power series.
     
    Last edited: Aug 15, 2008
  6. Aug 16, 2008 #5
    This are my thoughts, is this right?
     

    Attached Files:

  7. Aug 16, 2008 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Why do you think 1/(a_n-2) converges? Shouldn't you state a reason?
     
  8. Aug 16, 2008 #7
    If 1/(a_n-2) converges, than why shouldn't 1/(a_n-2) converge? I mean if a_n -> infinity than I don't think that 2 will bother him, no?
     
  9. Aug 16, 2008 #8

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    No, the 2 won't bother him. But you still have to show that. Set up a comparison test with something you know converges. Review my hint about this one.
     
  10. Aug 16, 2008 #9
    Yeah, I got you, thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: 2 in 1
  1. Integral of 1/1+25x^2 (Replies: 2)

Loading...