1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook