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The value of [(0.16)^(log(2.5)(1/3+1/3^2...

The value of `[(0.16)^(log_(2.5)(1/3+1/3^2+1/3^3+….+oo))]^(1/2)` is

A

`1`

B

`2`

C

`3`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
A
If a quadratic…………
`0.16^(log_(2.5((1)/(3)+(1)/(3^(2))+(1)/(3^(2))+...oo)))`
`= 0.16^(log_(2.5(((1)/(3))/(1-(1)/(3)))))=0.16^(log_(2.5((1)/(2))))`
`=0.16^(log_(2//5^(2)))= 1^(2) "root" = 4^((1)/(2))=2`
"Roots are" `= 2, A`
Sum of root `= 2+A=3`
`implies A = 1`
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