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If $x_n = \cos \left(\frac{\pi}{4^n}\right) + i \sin \left(\frac{\pi}{4^n}\right)$,then the product $x_1 x_2 x_3 \ldots \infty$ is equal to
In the given reaction,$A$ is:
$A$ $\xrightarrow{\text{Reduction}} B$ $\xrightarrow{HNO_2} C_2H_5OH$
$A$ $\xrightarrow{\text{Reduction}} B$ $\xrightarrow{HNO_2} C_2H_5OH$
If $\alpha = \frac{5}{2! 3} + \frac{5 \cdot 7}{3! 3^2} + \frac{5 \cdot 7 \cdot 9}{4! 3^3} + \ldots$,then $\alpha^2 + 4\alpha$ is equal to
The maximum value of $\frac{\log x}{x}, 0 < x < \infty$ is
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