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1+2/3+6/(3^2)+10/(3^3)+14/(3^4)+...

`1+2/3+6/(3^2)+10/(3^3)+14/(3^4)+`

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`S= 1 + 2/3 + 6/3^2 + 10/3^3 + ..........`(i)
`1/3 S = 1/3 + 2/3^2 + 6/3^3 + 10/3^4 + .... `(ii)
`(i)- (ii)`
`2s/3 = 2/3 + 2/3 + 4/3^2 + 4/3^3 + ......`
`2S/3 = 4(1/3 + 1/3^2 + 1/3^3 + ......)`
`2S/3 = (4 xx 1/3)/(1 -1/3)`
`= (4 xx 1 xx3)/(3 xx2) `
`2S/3 = 2`
...
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