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prove that : 2^n + 2^n-1 / 2^n+1 - 2^n = 3/2

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    ( 2 ^ n + 2 ^ ( n - 1 ) ) / ( 2 ^ ( n + 1 ) - 2 ^ n ) Multiply both sides by ( 2 ^ ( n + 1 ) - 2 ^ n )

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    ( 2 ^ n ) * 2 ^ ( n + 1 ) = 2 ^ ( 2 n + 1 )

    2 ^ ( n - 1 ) * (2 ^ ( n + 1 ) ) = 2 ^ 2 n

    2 ^ ( 2 n + 1 ) + 2 ^ 2 n = 3 * 4 ^ n


    2 ^ ( 2 n ) * 2 ^ ( 2 n ) = ( 2 ^ ( 2 n ) ) ^ 2 = 2 ^ ( 4 n )

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    ( 2 ^ n + 2 ^ ( n - 1 ) ) / ( 2 ^ ( n + 1 ) - 2 ^ n ) =

    2 ^ ( 2 n + 1 ) + 2 ^ 2 n / ( 2 ^ ( 2 n ) ) ^ 2 =

    3 * 4 ^ n / ( 2 * 4 ^ n ) = 3 / 2

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