The product of x 1 - 2 - x 1 - 4 - x 1 - 8 - equals

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Relation between AM,GM,HM for 2 Numbers

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The product of $x^{1 / 2} \cdot x^{1 / 4} \cdot x^{1 / 8} \dots \infty$ equals

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The infinite product $x^{\frac{1}{2}} . x^{\frac{1}{4}} . x^{\frac{1}{8}} . . . . . . . . . . .$ equals ___.

\frac{1}{a_{0}} + \frac{x}{a_{0} a_{1}} + \frac{x^{2}}{a_{0} a_{1} a_{2}} + \dots + \frac{x^{n}}{a_{0} a_{1} a_{2} \dots a_{n}} = \frac{1}{a_{0} -} \frac{a_{0} x}{a_{1} + x -} \frac{a_{1} x}{a_{2} + x -} \dots \frac{a_{n - 1} x}{a_{n} + x}

The product of infinite terms in $x^{\frac{1}{2}} . x^{\frac{1}{4}} . x^{\frac{1}{8}} . . . . . . . . . . . \infty$ is

(2^{1 / 4} \cdot 4^{1 / 8} \cdot 8^{1 / 6} \cdot 16^{1 / 32} - \dots \infty) = 2

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