作业帮 > 数学 > 作业

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( )

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/16 15:55:57
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( )
(1+2的1/32次方)(1+2的1/16次方)(1+2的1/8次)(1+2的1/4次)(1+2的1/2次)
结果是多少,要怎样做?
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))