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Point belongs to the boundary - real analysis

  1. Feb 21, 2015 #1
    Hello,
    I have some trouble to solve this exercise

    1. The problem statement, all variables and given/known data
    E={ (-1)n (8n+7)/(4n-1) : n ∈ℕ}
    Show that 2∈[PLAIN]http://www.ilemaths.net/img/smb-bleu/derivepartielle.gifE [Broken]
    2. Relevant equations


    3. The attempt at a solution
    We have to show that (2-r,2+r)∩ E ≠∅ and (2-r,2+r)∩ ℝ/E ≠∅
    If I take the part where (-1)n=1 i will note it E''
    We have
    (8n+7)/(4n-1)=2+9/(4n-1)
    I want to show that there is a point y so that y∈(2-r,2+r)∩ E'' i.e N :
    2-r<2+9/(4N-1)
    The thing is that we also have 2+r<2+9/(4N-1) but we are supposed to have 2+9/(4N-1) between 2-r and 2+r and then show that N ∃ by Archimedes' Principle, so what is wrong ?

    Thanks
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Feb 21, 2015 #2

    vela

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    Why do you think ##2+r < 2+\frac{9}{4N-1}##? You get to choose N so that ##2+\frac{9}{4N-1} < 2+r## holds.
     
  4. Feb 21, 2015 #3
    Thank you !
     
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