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Show that 9^(1/(4)).9^(1/(8)).9^(1/(16)....

Show that `9^(1/(4)).9^(1/(8)).9^(1/(16).) . .."to" oo = 2 `

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`4^((1)/(4)), 4^((1)/(4)), 4^((1)/(16)) ...."to" oo = 4^((1)/(4)+ (1)/(8) + (1)/(16) + "to" oo) `
Let ` S_(oo) = (1)/(4) + (1)/(8) + (1)/(16) + …"to" oo`
` therefore S_(oo) ((1)/(4))/(1 -(1)/(2)) = (1)/(4) xx 2 = (1)/(2)`
Now , LHS = ` 4^((1)/(2)) = 2 - ` RHS (proved)
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