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Show that X^((1)/(2)).X^((1)/(4)).X^((1...

Show that `X^((1)/(2)).X^((1)/(4)).X^((1)/(8))`... Upto `oo = X `

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`X^((1)/(2)),X^((1)/(4)),X^((1)/(8))`... Upto `oo = x `
`X^((1)/(2))+X^((1)/(4))+X^((1)/(8))`... Uptoo `oo`
`= X^(S)` , where `S = (1)/(2) + (1)/(4) + (1)/(8) + ...` upto `oo`
Here, S is the sum of an infinite G.P. wih ` a = (1)/(2) and r = (1)/(2)`
` therefore S = (a)/(1 -r) = ((1)/(2))/(1-(1)/(2)) = 1 `
Hence , required product = ` X^(S) = X^(1) = X` .
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