# Sequence converges to a limit

## Homework Statement

Show that a sequence Sn will converge to a limit L if and only if Sn - L converges to 0

## Homework Equations

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

## 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?

Related Calculus and Beyond Homework Help News on Phys.org
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