Please show the step-by-step derivation.

An infinite series of same-volume CSTR units can model the behavior of a PFR having the same total volume. Show that for a reaction that has a first-order reaction rate, the residence time, i, in a single CSTR in the series can be written as i=(1/k)[(CA0/CAN)(N1)1] where N is the number of CSTR units, CAO and CAN are the concentrations of component A entering unit 1, and leaving unit N respectively, and k is the specific rate of reaction (or the rate constant). Also, show that as N approaches infinity, N=(1/k)ln(CA0/CAN), which is the same as the residence time for a PFR having the same total volume as the CSTRs in series