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The sum of the infinite series 1+(1+1/5)...

The sum of the infinite series `1+(1+1/5)(1/2)+(1+1/5+1/(5^2))(1/(2^2))+...`

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`S=1+(1+1/5)(1/2)+(1+1/5+1/5^(2))(1/2^(2))`+… (1)
`therefore S/2=1/2+(1+1/5)(1/2^(2))+…(2)`
Subtracting (2) from (1), we get
`S/2=1+1/5xx1/2+1/5^(2)xx1/2^(2)+..`
`rArrS/2=1/(1-1/10)`
`rArrS=20/9`
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