Let G1, G2 be the geometric means of twoseries x1,x2,…xn;y1,y2…yn If G is the geometric meanof xi/yi,i=1,2,…n then G is equal to

G1=x1,x2∣…xn1/nand G2=y1,y2…yn1/nG=x1y1⋅x2y2…xnyn1/n=x1⋅x2…xn1/ny1⋅y2…yn1/n=G1G2

Let G1, G2 be the geometric means of twoseries x1,x2,…xn;y1,y2…yn If G is the geometric meanof xi/yi,i=1,2,…n then G is equal to

G1=x1,x2∣…xn1/nand G2=y1,y2…yn1/nG=x1y1⋅x2y2…xnyn1/n=x1⋅x2…xn1/ny1⋅y2…yn1/n=G1G2

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Let $G_{1}, G_{2}$ be the geometric means of two
series $x_{1}, x_{2}, \dots x_{n}; y_{1}, y_{2} \dots y_{n}$ If $G$ is the geometric mean
of $x_{i} / y_{i}, i = 1, 2, \dots n$ then $G$ is equal to

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$G_{1} - G_{2}$

$\log (G_{1} / G_{2})$

none of these

$\log G_{1} / \log G_{2}$

answer is D.

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Detailed Solution

$G_{1} = {(x_{1}, x_{2} ∣ \dots x_{n})}^{1 / n}$ and $G_{2} = {(y_{1}, y_{2} \dots y_{n})}^{1 / n}$

$G = {(\frac{x_{1}}{y_{1}} \cdot \frac{x_{2}}{y_{2}} \dots \frac{x_{n}}{y_{n}})}^{1 / n} = \frac{{(x_{1} \cdot x_{2} \dots x_{n})}^{1 / n}}{{(y_{1} \cdot y_{2} \dots y_{n})}^{1 / n}} = \frac{G_{1}}{G_{2}}$

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Let G1, G2 be the geometric means of twoseries x1,x2,…xn;y1,y2…yn If G is the geometric meanof xi/yi,i=1,2,…n then G is equal to

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Let $G_{1}, G_{2}$ be the geometric means of two
series $x_{1}, x_{2}, \dots x_{n}; y_{1}, y_{2} \dots y_{n}$ If $G$ is the geometric mean
of $x_{i} / y_{i}, i = 1, 2, \dots n$ then $G$ is equal to