Let Eo an and E, bn be two series i. If Eo an: o bn converge...

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Let Eo an and E, bn be two series i. If Eo an: o bn converge to a and 3 respectively and their Cauchy product converges to 8, then show that a3 = 6. ii. If Eo an converges absolutely to a and o bn converges to B. then show that their cauchy product converges to a3. iii. If Eo an, E bn converge absolutely to a and B respectively, then show that their cauchy product converges absolutely to aß. iv. Give examples and counter examples. Let Eo an and E, bn be two series i. If Eo an: o bn converge to a and 3 respectively and their Cauchy product converges to 8, then show that a3 = 6. ii. If Eo an converges absolutely to a and o bn converges to B. then show that their cauchy product converges to a3. iii. If Eo an, E bn converge absolutely to a and B respectively, then show that their cauchy product converges absolutely to aß. iv. Give examples and counter examples.