Aptitude

Abstract

23. In an imaginary water filtration process a fraction of 1 /n of an impurity is removed in the first pass of the water through the system. In each succeeding pass, the amount of impurity removed is 1 /n of the amount removed in the preceding pass. Show that if n = 2 the water can be made arbitrarily pure but if n = 3, at least half of the impurity will remain.