Question

the sequence (n) has limit point?
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Answer 1

Answer:

A sequence whose set of limit points is the set of natural numbers. Consider the sequence (vn) whose initial terms are 1,1,2,1,2,3,1,2,3,4,1,2,3,4,5,… which proves that m is a limit point of (vn).

Answer 2

Answer:

If l=un for infinitely many values of n then l is a limit point of the sequence u. As in the case of sets of real numbers, limit points of a sequence may also be called accumulation, cluster or condensation points.

Step-by-step explanation:

• If l=un for infinitely many values of n then l is a limit point of the sequence u. As in the case of sets of real numbers, limit points of a sequence may also be called accumulation, cluster or condensation points.
• The sequence defined by $a_{n}=(-1)^n$ looks like this:
  $[1,-1,1,-1,1,-1,...]$
  ,that is assuming n starts at 0. Since the sequence keeps oscillating between 1 and −1, it never gets "close" to any point, and thus it does not have a limit.
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