Evaluate- 312-314-318-

The correct option is B 3 Now, 3^1/2.3^1/4.3^1/8......∞ =3^1/2+1/4+1/8+......∞ =3^1/2+1/2^2+1/2^3+......∞ =3^1/2/1 1/2 =3^1 =3 ...

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Byju's Answer

Standard IX

Mathematics

Property 6

Evaluate: 31...

Question

Evaluate:
$3^{\frac{1}{2}} {.3}^{\frac{1}{4}} {.3}^{\frac{1}{8}} . . . . . . \infty =$

\sqrt{3}

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3

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9

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none of these

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Solution

The correct option is B $3$
Now,
$3^{\frac{1}{2}} {.3}^{\frac{1}{4}} {.3}^{\frac{1}{8}} . . . . . . \infty$
$= 3^{\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + . . . . . . \infty}$
$= 3^{\frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + . . . . . . \infty}$
$= 3^{\frac{\frac{1}{2}}{1 - \frac{1}{2}}}$
$= 3^{1}$
$= 3$ .

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Evaluate:312.314.318......∞=

The correct option is B 3Now,312.314.318......∞=312+14+18+......∞=312+122+123+......∞=3121−12=31=3.

Evaluate:
$3^{\frac{1}{2}} {.3}^{\frac{1}{4}} {.3}^{\frac{1}{8}} . . . . . . \infty =$