Question

化简（1+2的1/32次方）（1+2的1/16次方）（1+2的1/8次） ,结果是( )

Answer 1

原式

=(1+2^(1/32))(1+2^(1/16))(1+2^(1/8))(1+2^(1/4))(1+2^(1/2))

=[(1+2^(1/32))(1+2^(1/16))(1+2^(1/8))(1+2^(1/4))(1+2^(1/2))*((1-2^(1/32))]/(1-2^(1/32))

=[(1-2^(1/16))(1+2^(1/16))(1+2^(1/8))(1+2^(1/4))(1+2^(1/2))]/(1-2^(1/32))

=[(1-2^(1/8))(1+2^(1/8))(1+2^(1/4))(1+2^(1/2))]/(1-2^(1/32))

=[(1-2^(1/4))(1+2^(1/4))(1+2^(1/2))]/(1-2^(1/32))

=[(1-2^(1/2))(1+2^(1/2))]/(1-2^(1/32))

=(1-2)/(1-2^(1/32))

=-1/(1-2^(1/32))