Let{an}[infinity]n=1be a sequence. A real numberxis alimit point(sometimes called anaccumulation point) if there is a subsequence{ank}[infinity]k=1which converges tox.(a) How many limit points do the following sequences have?(i){(−1)n}[infinity]n=1(ii)an= 10 ifn= 1, . . . ,100 andan=1nifn >100.(b) Construct a sequence that does not have a limit point.(c) Construct a sequence with exactly 2 limit points.(d) Construct a sequence that has exactly one limit point, but which does not con-verge.