i have that lim x_n=lim y_n=a(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Sequence question.

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