Task* 46: Solve one of the following subtasks: (a) Show, lim (1 + 2)" = Σo (b) If (an)nen is a zero sequence with 0 # an eRso for all n

e N, then the following applies lim (1 + an) = e. (c) For x € R20 show lim0 (1 + )" = e. AR Notes: a. if sn denotes the nth partial sum of the series and tn = (1+), then let tn Ssn and limn-00 tn 2 sm for all M. Note that the convergence of the two sequences (sn)nen and (tn)n21 is already known, see task 29. For B., divide the sequence into partial sequences of (tn)n >1.