Prove that : Find the sum of the infinit...

Prove that : Find the sum of the infinite series
`1+(2)/(3).(1)/(2)+(2.5)/(3.6)((1)/(2))^(2)+(2.5.8)/(3.6.9)((1)/(2))^(3)+......oo`

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The correct Answer is:

`root(3)(4)`

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