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Prove that: (i)\ sqrt(1/4)+\ (0. 01)^(-1...

Prove that: `(i)\ sqrt(1/4)+\ (0. 01)^(-1/2)-\ (27)^(2/3)=3/2` `(ii)\ (2^n+\ 2^(n-1))/(2^(n+1)-2^n)=3/2` `(i)\ sqrt(1/4)+\ (0. 01)^(-1/2)-\ (27)^(2/3)=3/2`

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1408718 `=1/2+(1/100)^(-1/2)-3^(3xx2/3)`
`=1/2+100^(-1/2)-3^2`
`=1/2+10-9`
`=1/3`
(ii) `(2^n+\ 2^(n-1))/(2^(n+1)-2^n)=3/2`
`=(2^n+\ 2^(n-1))/(2^(n+1)-2^n)`
`=(2^(n+n-1))/(2^(n+1)-2^n)`
`=2^(2n-1-n-1-n`
`(iii)sqrt(1/4)+\(0. 01)^(-1/2)-\ (27)^(2/3)=3/2`L.H.S
`sqrt(1/4)+ (0.01)^-(1/2) − (27)^3`
`= 1/2 + 1/(0.01)^(1/2) (3^3)^(2/3)`
`=1/2 +1/((0.1)^2) xx 1/2 -((3)^3)^2/3`
`= 1/2 + 1/(0.1)^1 - (3)^2`
`=1/2 + 1/(0.1)- 9`
`=3/2`
`= R.H.S`
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