Consider the geometric progression whose first term is 7 and whose common ratio is −21. For positive integers n, let Sn be the sum of the first n terms.
a. (i) Obtain a simplified expression for Sn in terms of n.
b. (ii) Show that S2n=314(1−(−21)2n).
c. (iii) Using your result from part (i), find the least integer n such that ∣S∞−Sn∣<0.0001, where S∞ denotes the sum to infinity of the progression. Present a clear justification for your answer.