Find the value of $2^{1 / 4} . 4^{1 / 16} . 8^{1 / 48} . . . . . \infty$ .

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Solution

$2^{\frac{1}{2}} {.4}^{\frac{1}{16}} {.8}^{\frac{1}{48}}$
$2^{\frac{1}{4}} {.2}^{\frac{1}{8}} {.2}^{\frac{1}{16}}$
$2^{(\frac{1}{4} + \frac{1}{8} + . .)}$
$2^{(\frac{1 / 4}{1 - \frac{1}{2}})} = 2^{2} = 4$

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Similar questions

2^{\frac{1}{4}} . 4^{\frac{1}{8}} . 16^{\frac{1}{16}} . 256^{\frac{1}{32}}

2^{1 / 4} {.4}^{1 / 8} {.8}^{1 / 16} . . . . \infty

2^{\frac{1}{4}} {.4}^{\frac{1}{8}} {.8}^{\frac{1}{16}} {.16}^{\frac{1}{32}} . . . . \infty

2^{\frac{1}{4}} {.4}^{\frac{1}{8}} {.8}^{\frac{1}{16}} . 16^{\frac{1}{32}} . . . . . . . . . . . . . . . = 32^{\frac{1}{m}}

m

2^{\frac{1}{4}} . 4^{\frac{1}{8}} . 8^{\frac{1}{16}} . 16^{\frac{1}{32}} . . . . . .

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