5. a) Write the sum ofn terms in a geometric progression with a first term a and a common ratio r as S. = atar +ar2 +... +arn- 1 Subtract rS, from S, and rearrange to obtain the formula for the sum of n terms: a(1 - rn ) 1 - r b) Under what conditions does the sum ofn terms of a geometric pro- gression tend to a finite sum asn tends to infinity? What is this sum? c) Obtain an expression for the sum of the weights in an EWMA if we specify a, = x, in Equation (3.15). d) Suppose x, happens to be a sequence of independent variables with a constant mean and a constant varianceo2. What is the variance ofa if we specify a, = x, in Equation (3.15)