Question: Topic: (SUBSEQUENCES and ACCUMULATION POINTS) Consider the interval (0,5] . Construct a sequence of real numbers (un ) in this interval such that it has

Topic: (SUBSEQUENCES and ACCUMULATION POINTS)

Consider the interval (0,5] . Construct a sequence of real numbers
(un
) in this interval such that it has two subsequences, both of which
are Cauchy sequences, but such that one of subsequences converges
in this interval and the other does not. Identify an accumulation point
of sequence (un
) .

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