Help with proving a sequence converges

  • Thread starter jarvegg
  • Start date
  • #1
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I am really stuck on this on

Let sn and tn be sequences. Suppose that lim sn = L (where s is a real number) and lim |sn - tn| = 0. Prove that lim tn = L.

I think this is going in the right way but i am not sure. If the lim an = A, then lim |an - A| = 0.

any help would be very nice.
 

Answers and Replies

  • #2
3
0
Help proving a sequesnce converges

I am really stuck on this on

Let sn and tn be sequences. Suppose that lim sn = L (where s is a real number) and lim |sn - tn| = 0. Prove that lim tn = L.

I think this is going in the right way but i am not sure. If the lim an = A, then lim |an - A| = 0.

any help would be very nice.
 
  • #3
lurflurf
Homework Helper
2,440
138
let N be so large that
|s_n|<epsilon/2
|s_n-t_n|<epsilon
what can you say about
|t_n|
?
hint
|A-B|<=|A|+|B|
 
  • #4
3
0
I know how to do a N Epsilon proof but don't you have to have |s_n + t_n - (s + t)| < epsilon??

And that is to show that the lim (s_n + t_n) = s + t. I need to know lim |s_n - t_n| = 0. i guess i am unsure how the abs effect the proof.
 
  • #6
HallsofIvy
Science Advisor
Homework Helper
41,833
964
I have merged the two threads.
 

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