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  4. The product of x1 / 2 ⋅ x1 / 4 ⋅ x1 / 8 ldots ∞ equals

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

Bihar CECEBihar CECE 2011

Solution:

$x^{(1 / 2+1 / 4+1 / 8+\ldots(0 \infty)}=x^{\left(\frac{1 / 2}{1-1 / 2}\right)}=x$