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Sequence converges to a limit

  1. May 30, 2010 #1
    1. The problem statement, all variables and given/known data
    Show that a sequence Sn will converge to a limit L if and only if Sn - L converges to 0


    2. Relevant equations

    {Sn} converges to L if and only if {Sn - L } converges to 0

    3. The attempt at a solution

    Is it enough to just say

    {Sn} converges to L if and only if |Sn - L| < \epsilon if and only if |(Sn - L) - 0| < \epsilon if and only if {Sn - L}$ converges to 0

    I'm learning this off a random pdf so I don't have the answers.

    Is this enough? Any suggestions would be appreciated. Also is there a way to turn on Latex?
     
  2. jcsd
  3. May 30, 2010 #2
    since Sn converges to L, then :
    lim Sn = L ... (1)
    for the sequence {Sn-L}
    lim ( Sn - L ) = lim Sn - lim L = L - L = 0
    so {Sn-L} converges to 0

    its looks easy for me, or i missed something :S
     
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