a) Let {zn} be a sequence of complex numbers, with Re(2n) 2 0 for all n...

  

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a) Let {zn} be a sequence of complex numbers, with Re(2n) 2 0 for all n E N. Writing Zn = xn+iyn, given that the series Eo n is convergent, prove that each of the following n=D0 series is absolutely convergent: 1) Σ ii) Eo "nYn- b) If in addition to a) above, the series is also convergent, prove that each of the n=0 "n following hold: i) The series is absolutely convergent. ii) The series E is absolutely convergent. a) Let {zn} be a sequence of complex numbers, with Re(2n) 2 0 for all n E N. Writing Zn = xn+iyn, given that the series Eo n is convergent, prove that each of the following n=D0 series is absolutely convergent: 1) Σ ii) Eo "nYn- b) If in addition to a) above, the series is also convergent, prove that each of the n=0 "n following hold: i) The series is absolutely convergent. ii) The series E is absolutely convergent.