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Answer :
Final answer:
In a sequence, a subsequence is obtained by selecting some terms from the original sequence in a specific order. The limit inferior and limit superior of a sequence are the values that the sequence approaches as n goes to infinity. The correct answers are: A. Lim inf an; lim sup an.
Explanation:
Let (an) be a sequence of real numbers. In a sequence, a subsequence is obtained by selecting some terms from the original sequence in a specific order. The given question asks about the existence of a subsequence (ank) such that the limit of (ank) as n goes to infinity is equal to the limit of the original sequence (an) as n goes to infinity.
The correct answers are: A. Lim inf an; lim sup an. The limit inferior (lim inf) and limit superior (lim sup) of a sequence are the values that the sequence approaches as n goes to infinity. The lim inf an and lim sup an are subsequential limits of the sequence.
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