Sequence converges to a limit

  • Thread starter ocohen
  • Start date
  • #1
24
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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?
 

Answers and Replies

  • #2
42
0
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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