Question: Let (an) be a decreasing sequence of real numbers converging to 0 and suppose that an diverges. Construct a divergent series bn with bn >

Let (an) be a decreasing sequence of real numbers converging to 0 and suppose that ∑an diverges. Construct a divergent series ∑bn with bn > 0 such that lim(bn/an)= 0; hence ∑bn diverges less rapidly than ∑an. [Let bn := an/√An where An is the nth partial sum of ∑an.]

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