Help with proving a sequence converges

[jarvegg]

I am really stuck on this on

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

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

any help would be very nice.

 

[jarvegg]

Help proving a sequesnce converges

I am really stuck on this on

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

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

any help would be very nice.

 

[lurflurf]

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|

 

[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.

 

[tiny-tim]

Duplicate thread!

Duplicate of https://www.physicsforums.com/showthread.php?t=304540"

 

[HallsofIvy]

I have merged the two threads.