Please can you help me whit this question I can't figure it out?
$l_1$ is an adherent point of $(u_n)$ and $l_2$ is an adherent point of $(v_n)$ can we say that $l_1+l_2$ is an adherent point of $(u_n+v_n)$?
Please can you help me whit this question I can't figure it out?
$l_1$ is an adherent point of $(u_n)$ and $l_2$ is an adherent point of $(v_n)$ can we say that $l_1+l_2$ is an adherent point of $(u_n+v_n)$?
I’m assuming that by adherent point of the sequence you mean what I would call a cluster point: a point that is the limit of some subsequence of the given sequence.
HINT: What if the sequences are $\langle 0,1,0,2,0,3,0,4,0,5,\dots\rangle$ and $\langle1,0,2,0,3,0,4,0,5,\dots\rangle$?