Sol: Here, given that,
.
This implies that the sequences { } and {} are bounded.
Also, given that,
When
we get,
Which follows the inequality.
Now, we will proof the inequality for
Let,
Also, we know that, a real number A is the limit superior of a bounded sequence {} if and only if for each there exists a positive integer m such that
So, here, for some there exists positive integers such that
and
.
Therefore, for all , we get,
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In = 0, yn = 0.
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