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The sum of 0.2+0.004+0. 00006+0. 0000008...

The sum of `0.2+0.004+0. 00006+0. 0000008+...` to `oo` is

A

`200/891`

B

`2000/9801`

C

`1000/9801`

D

`2180/9801`

Text Solution

Verified by Experts

The correct Answer is:
D
`S=2/10+4/10^(3)+6/10^(5)+8/10^(7)+..` to `oo` (1)
`=(2/10)/(1-1/10^(2))+(2xx(1/10^(2)))/((1-1/10^(2))^(2))`
`=20/99+200/9801`
`=2180/9801`
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