So, lets say i have a sequence a(n). A sequence can have a lim superior (greatest cluster point) or lim inferior (lowest cluster point), only if the sequence is bounded, right?
so, given a(n):= (1 + (-1)^n nē) / (2 + 3n + nē)
with n >> infinity, lim a(n) diverges between -infinity and infinity therefor it isn't bounded and has no lim superior or lim inferior. correct?
and a more tricky sequence definied by:
a(3n-2):= 3 + 1/n
a(3n):= - 1/nē
my (correct/incorrect) answer:
the sequence a(n) has two cluster points, a limit inferior of the value 0 and a limit superior of the value 3.
is everything i mentioned above correct?