Question:
The product $2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 16^{\frac{1}{128}} \ldots$ to $\infty$ is equal to:
Correct Option: 1
Solution:
$2^{\frac{1}{4}}+\frac{2}{16}+\frac{3}{48}+\ldots \ldots \infty$
$=2^{\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\ldots \ldots \infty}=\sqrt{2}$
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