Question

化简：（1+2^1/32）(1+2^1/16)(1+2^1/8)(1+2^1/4)(1+2^1/2)

Answer 1

原式左乘一个[1-2^(1/32)]/[1-2^(1/32)]得

[1-2^(1/32)]*[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^(1/16)]*[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/[2^(1/32)-1]