Let an and o bn be two series i. If E-o an, E=0 bn converge to...

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Let an and o bn be two series i. If E-o an, E=0 bn converge to a and 3 respectively and their Cauchy product converges to 6, then show that aß = 6. ii. If E-o an converges absolutely to a and E=0 bn converges to 3, then show that their cauchy product converges to a3. iii. If Eo an, E, b, converge absolutely to a and 3 respectively, then show that their cauchy product converges absolutely to aß. m%3D0 iv. Give examples and counter examples. Let an and o bn be two series i. If E-o an, E=0 bn converge to a and 3 respectively and their Cauchy product converges to 6, then show that aß = 6. ii. If E-o an converges absolutely to a and E=0 bn converges to 3, then show that their cauchy product converges to a3. iii. If Eo an, E, b, converge absolutely to a and 3 respectively, then show that their cauchy product converges absolutely to aß. m%3D0 iv. Give examples and counter examples.