(a) Suppose that Σa_n and Σb_n are series with positive terms and Σb_n is c…

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(a) Suppose that Σa_n and Σb_n are series with positive terms and Σb_n is convergent. Prove that if lim_n →∞ a_n/b_n=0 then Σa_n is also convergent. (b) Use part (a) to show that the series converges. (i) ∑_n=1^∞ lnn/n^3 (ii) ∑_n=1^∞ lnn/√(n) e^n

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