Consider a sequence (bn)1 of non-zero real numbers. By definition, the infinite product Ibn converges if...

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Consider a sequence (bn)1 of non-zero real numbers. By definition, the infinite product Ibn converges if the sequence (Pn)1 where n= n Pn=IIbk k=1 converges to some non-zero real number. a) Assume br > 0 for all n N. Prove that bn converges if and only if converges. b) Calculate n=1 In ba II exp (0.5"). n=1 Consider a sequence (bn)1 of non-zero real numbers. By definition, the infinite product Ibn converges if the sequence (Pn)1 where n= n Pn=IIbk k=1 converges to some non-zero real number. a) Assume br > 0 for all n N. Prove that bn converges if and only if converges. b) Calculate n=1 In ba II exp (0.5"). n=1