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The value of 2^(1/4).4^(1/8).8^(1/16),...

The value of `2^(1/4).4^(1/8).8^(1/16),,,,,,,oo` is equal to.

A

1

B

2

C

`3//2`

D

4

Text Solution

Verified by Experts

The correct Answer is:
b
`2^(1//4) * 4^(1//8) ...oo = 2^(1/4+2/8+3/16+...oo=(2)^(1/4){1+2/2+3/(2^(2))+4/(2^(3))+...}`
`= (2)^(1/4 {1/(1-1//2)+(1*1//2)/((1-1//2)^(2))})=2^(1/4(2+2))=2`
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