Question

Example of an unbounded sequence with two subsequence one of which convergent and other is divergent

Answer 1

Answer:

Step-by-step explanation:

Consider the trivial example (xn)n∈N given by xn=n, which obviously does not converge. This sequence has no convergent subsequence, so the condition from the theorem holds vacuously for any x (i.e. for any x∈R, any convergent subsequence of (xn) converges to x).

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