# Help with proving a sequence converges

1. Apr 2, 2009

### jarvegg

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.

2. Apr 2, 2009

### jarvegg

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. Apr 2, 2009

### lurflurf

let N be so large that
|s_n|<epsilon/2
|s_n-t_n|<epsilon
|t_n|
?
hint
|A-B|<=|A|+|B|

4. Apr 3, 2009

### jarvegg

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.

5. Apr 3, 2009

### tiny-tim

Last edited by a moderator: Apr 24, 2017
6. Apr 3, 2009

### HallsofIvy

Staff Emeritus
I have merged the two threads.