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Proving a limit

  1. Apr 7, 2009 #1
    how do i prove this limit?

    lim
    n->inf [tex]\frac{0+2+4+....2n}{1+3+....(2n+1)}[/tex]=1

    i think that its because of the fact that 2n is so big compared to the rest, and compared to the 1 in (2n+1) that their affect on the lim is none, is this correct?
    how do i write this mathematically>
     
  2. jcsd
  3. Apr 7, 2009 #2
    You could always find a closed form expression for the sum of the first n even integers and the first n odd integers, and then substitute those.

    One could also note that the bottom line is always (n+1) more than the top line... and then get the expression for the even integers, and use l'Hopitals rule and keep the high-order terms.
     
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