ii) xn √n-1 √n+1' iii) x₂ = (-1)"+¹ + 1/1.

A: Every bounded sequence has convergent subsequence.

A: To Find: A topic relating to the Boundedness of Convergent Sequences for a final project.

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A: We find the limit of the an th term. limx→∞(an)=limx→∞1+(-1)nn=1+limx→∞(-1)nn=1+0=1

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A: Every convergent sequence is a bounded sequence, that is the set {xn : n ∈ N} is bounded. Remark :…

A: The given statement, "If a sequence is convergent then it is bounded and monotone." is false. Let is…

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A: Given sequence {2n+13-n}={un} (say)