# Sequence converges to a limit

1. May 30, 2010

### ocohen

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. May 30, 2010

### System

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