Posted by tuhituhi on Friday, March 29, 2013 at 4:20am.
( 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