Let an AP with positive first term a and positive common difference d and a GP with the same first term a and common ratio r>1 be given.
a. (i) Prove that there can be at most one positive integer n for which the sums of the first n terms of the two progressions are equal.
b. (ii) If such an integer n0 exists, prove that for every n>n0 the sum of the GP exceeds the sum of the AP.