( 1 + 2 ^ -1/8 )( 1 + 2 ^ -1/4 )( 1 + 2 ^ -1/2 )求简便方法!
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![( 1 + 2 ^ -1/8 )( 1 + 2 ^ -1/4 )( 1 + 2 ^ -1/2 )求简便方法!](/uploads/image/z/6890458-58-8.jpg?t=%28+1+%2B+2+%5E+-1%2F8+%29%28+1+%2B+2+%5E+-1%2F4+%29%28+1+%2B+2+%5E+-1%2F2+%29%E6%B1%82%E7%AE%80%E4%BE%BF%E6%96%B9%E6%B3%95%21)
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( 1 + 2 ^ -1/8 )( 1 + 2 ^ -1/4 )( 1 + 2 ^ -1/2 )求简便方法!
( 1 + 2 ^ -1/8 )( 1 + 2 ^ -1/4 )( 1 + 2 ^ -1/2 )
求简便方法!
( 1 + 2 ^ -1/8 )( 1 + 2 ^ -1/4 )( 1 + 2 ^ -1/2 )求简便方法!
( 1 + 2 ^ -1/8 )( 1 + 2 ^ -1/4 )( 1 + 2 ^ -1/2 )
=(1 - 2^-1/8)( 1 + 2 ^ -1/8)( 1 + 2 ^ -1/4 )( 1 + 2^-1/2)/(1 - 2^-1/8) 分子分母同乘以一个1 - 2^-1/8
= (1-2^-1/4)( 1 + 2 ^ -1/4 )( 1 + 2^-1/2)/(1 - 2^-1/8)
=(1-2^-1/2)( 1 + 2^-1/2)/(1 - 2^-1/8)
=(1-2^-1)/(1 - 2^-1/8)
=1/2 / (1 - 2^-1/8)
=自己化简吧~