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If the sum to infinty of the series , 1+...

If the sum to infinty of the series , `1+4x+7x^(2)+10x^(3)+….`, is `(35)/(16)`, where `|x| lt 1`, then `'x'` equals to

A

`19//7`

B

`1//5`

C

`1//4`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `S=1+4x+7x^(2)+10x^(3)+`…..
`x.S=x+4x^(2)+7x^(3)+`…….
Subtracting
`S(1-x)=1+3x+3x^(2)+3x^(3)+`……….
`S(1-x)=1+3x((1)/(1-x))|x| lt 1`
`:.S=(1+2x)/((1-x)^(2))`
Given `(1+2x)/((1-x)^(2))=(35)/(16)`
`implies16+32x=35+35x^(2)-70x`
`implies(5x-1)(7x-19)=0`
But `|x| lt 1 :. x=(1)/(5)`
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