Let {a;} and {b;} be any sequences. Consider the following statements: Σα di If 0 < ai < b; for all i 245 and diverges, then with I. E(b: + 2) certainty it is satisfied that is also divergent. 2 II. If bj >0 for all i 224 and lim 9, Σ is convergent. then with certainty it is satisfied that

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A: We have to determine whether the statement is true or false.

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Q: converges, because 0 < 1 and an %3D debook 2n + 1 2n +1 2n +1 Room

A: We have to choose the true or false

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A: It is given that:

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A: Given, xn  be a sequence  in a metric space X and  xn has a subsequence xnjthat converges to  a…

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A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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Q: b) Give an easy alternative proof of the Bolzano-Weierstrass Theorem.

A: As directed in the question, answer of only part b is provided below :   (b) Bolzano-Weierstrass…

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