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Let S=4/19+44/(19)^2+444/(19)^3+...oo th...

Let S=`4/19+44/(19)^2+444/(19)^3+...oo` then find the value of S

A

`40//9`

B

`38//81`

C

`36//171`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`S=4/19+44/19^(2)+444/19^(3)+…` (1)
`rArr1/19S=4/19^(2)+44/19^(3)+…` (2)
Subtracting (2) from (1), we get
`18/19S=4/19+40/19^(2)+400/19^(3)+…`
`=(4/19)/(1-10/19)=4/9`
`rArrS=38/81`
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