- #1
MathematicalPhysicist
Gold Member
- 4,699
- 371
i have that lim x_n=lim y_n=a
and we have the sequence (x1,y1,x2,y2,...)
i need to show that this sequence (let's call it a_n) converges to a.
well in order to prove it i know that if a_n has a unique partial limit then it converges to it to it, but how do i show here that it has a unique partial limit?
i mean if we take the subsequences in the even places or the odd places then obviously those subsequences converges to the same a, but i need to show this is true for every subsequence, how to do it?
thanks in advance.
and we have the sequence (x1,y1,x2,y2,...)
i need to show that this sequence (let's call it a_n) converges to a.
well in order to prove it i know that if a_n has a unique partial limit then it converges to it to it, but how do i show here that it has a unique partial limit?
i mean if we take the subsequences in the even places or the odd places then obviously those subsequences converges to the same a, but i need to show this is true for every subsequence, how to do it?
thanks in advance.