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the value of [(0.16)^(log0.25 (1/3+1/3^2...

the value of `[(0.16)^(log_0.25 (1/3+1/3^2+1/3^3+....................+oo))]^(1/2)` is

A

1

B

-1

C

0

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
d
` [ (0.16) ^(log_(0.25)(1/3+1/(3^(2))+1/(3^(3))+...))]^(1//2)`
` = [ (0.16)^(log_(0.25)((1//3)/(1-1//3)))]^(1//2) = [ (0.16)^(log_((0.5)^(2))0.5)]^(1//2)`
`= [ (0.16)^(1//2)]^(1//2) = (0.4)^(1//2) = 2/(sqrt(10))`
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