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Prove that (9^(1/3).9^(1/9).9^(1/27).......

Prove that `(9^(1/3).9^(1/9).9^(1/27)............oo)=3`

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`9^((1)/(3)), 9^((1)/(9)), 9^((1)/(27)) ...."to" oo = 9^((1)/(3)+ (1)/(9) + (1)/(27) + "to" oo) `
Let ` S_(oo) = (1)/(3) + (1)/(9) + (1)/(27) + … "to" oo`
` therefore S_(oo) = ((1)/(3))/(1 - (1)/(3)) = (1)/(3) xx (3)/(2) = (1)/(2)`
` therefore ` Required sum ` 9^((1)/(2) = 3 `
Hence Proved
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