Suppose that \(v_{1}, v_{2}, \ldots, v_{n}\) are positive numbers. The arithmetic mean and the geometric mean of these numbers are, respectively,

(a) It is always true that \(v_{A} \geq v_{G}\). Prove this inequality for \(n=2\).

(b) If \(r_{1}, r_{2}, \ldots, r_{n}\) are rates of return of a stock in each of \(n\) periods, the arithmetic and geometric mean rates of return are likewise

Suppose \(\$ 40\) is invested. During the first year it increases to \(\$ 60\) and during the second year it decreases to \(\$ 48\). What are the arithmetic and geometric mean rates of return over the 2 years?

(c) When is it appropriate to use these means to describe investment performance?

Transcribed Image Text:

VA= Vi and VG = 12 Vi 1/n