Let G_1 and G_2 be the geometric means of two | vedclass

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(D) Given that $G_1 = (x_1 	imes x_2 	imes \dots 	imes x_n)^{1/n}$ and $G_2 = (y_1 	imes y_2 	imes \dots 	imes y_n)^{1/n}$.The geometric mean $G

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$G_1/G_2$

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(D) Given that $G_1 = (x_1 	imes x_2 	imes \dots 	imes x_n)^{1/n}$ and $G_2 = (y_1 	imes y_2 	imes \dots 	imes y_n)^{1/n}$.The geometric mean $G$ of the series $\frac{x_i}{y_i}$ is defined as:$G = \left( \frac{x_1}{y_1} 	imes \frac{x_2}{y_2} 	imes \dots 	imes \frac{x_n}{y_n} ight)^{1/n}$$G = \frac{(x_1 	imes x_2 	imes \dots 	imes x_n)^{1/n}}{(y_1 	imes y_2 	imes \dots 	imes y_n)^{1/n}}$Substituting the values of $G_1$ and $G_2$:$G = \frac{G_1}{G_2}$

Let $G_1$ and $G_2$ be the geometric means of two series $x_1, x_2, \dots, x_n$ and $y_1, y_2, \dots, y_n$ respectively. If $G$ is the geometric mean of the series $\frac{x_i}{y_i}$ where $i = 1, 2, \dots, n$,then what is $G$ equal to?

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