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

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

Text Solution

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We have,
`6^(1//2)xx6^(1//4)xx6^(1//8)…oo`
`=6^([1//2+1//4+1//8+… "to"oo]`
`=6^([(1//2)//(1-1//2)])=6^(1)=6`
`[because1/2+1/4+1/8+…"to"oo=(1//2)/(1-1//2)=1]`
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