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I just dont get this proof of convergence of even and uneven sequence coeffi. ?

  1. Dec 4, 2011 #1
    1. The problem statement, all variables and given/known data
    Show that if Lim(n-->inf.)(a_(2n)-->L) and Lim(n-->inf.)(a_(2n+1)-->L) then Lim(n-->inf.)(a_n-->L).

    3. The attempt at a solution
    I just dont get this; I can see the big picture though. If the odd coeffictions of a sequences goes towards one the same number as the even coefficients, then ultimately the complete sequence must also be approaching that number.

    But the proof in my textbooks uses the formal limit defintion of the limit of a sequence. It states the the odd part has an N_1 and the even part has N_2 and so on .. you guys know the definition:) But then it goes on into something about a "max" of those two numbers, which i have abselutely no idea what is?? And looking at it, i cannot seem to understand it .. Its really annoying, since all the assignemts were going well. I thought i had these simple infinite series, but now i am completely blank lol .. I have no idea how to formulate a proof of my understanding.

    It may be good to mention, that i am a 17 year old high school student on my own, self designes study course, since the HS math is rather boring^^ Maybe i am missing a key component in my mathematical knowledge to do this proof, or i may simply not be smart enough ..

    Could you guys elaborate a bit ? :) I'm sorry i haven't provided an attempt, but as i said, im rather blank ..
     
  2. jcsd
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