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The sum of the series 1 +3/4+7/16 +15/64...

The sum of the series `1 +3/4+7/16 +15/64+31/256+....` to infinite is:

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`=4sum_(n=1)^oo 2^n/4^n-4sum_(n=1)^oo1/4^n`
`4sum_(n=1)^oo 1/2^n-4sum_(n=1)^oo 1/4^n`
`4[sum_(n=1)^oo 1/2^n-sum_(n=1)^oo 1/4^n]`
`4[(1/2)/(1-1/2)-(1/4)/(1-1/4)]`
`4[(1/2)/(1/2)-(1/4)/(3/4)]`
`4[1-1/3]=4*2/3=8/3`.
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