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Prove that 6^(1//2)xx6^(1//4)xx6^(1//8)....

Prove that `6^(1//2)xx6^(1//4)xx6^(1//8)...oo=6.`

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We observe here that `(1/2+1/4+1/8+...∞)` is an infinite geometric series
in which `a=1/2` and `r=1/2` `
` such that `|r|<1`.
So, this sum is given by `S=(1/2)/(1−1/2)=(1/2)/(1/2)=1 ...(i) `
∴`6^(1/2).6^(1/4).6^(1/8)...∞`
=`6^(1/2+1/4+1/8+...∞)=6^1=6`
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