2/(1-x) 式中2为分子,1-x为分母
2/(1-x)+2/(1+x)+4/(1+x^2)+8/(1+x^4)+16/(1+x^8)+32/(1+x^16)
=2(1+x)/(1-x^2)+2(1-x)/(1-x^2)+4/(1+x^2)+8/(1+x^4)+16/(1+x^8)+32/(1+x^16)
=4/(1-x^2)+4/(1+x^2)+8/(1+x^4)+16/(1+x^8)+32/(1+x^16)
=4(1+x^2)/(1-x^4)+4(1-x^2)/(1-x^4)+8/(1+x^4)+16/(1+x^8)+32/(1+x^16)
=8/(1-x^4)+8/(1+x^4)+16/(1+x^8)+32/(1+x^16)
=8(1+x^4)/(1-x^8)+8(1-x^4)/(1-x^8)+16/(1+x^8)+32/(1+x^16)
=16/(1-x^8)+16/(1+x^8)+32/(1+x^16)
=16(1+x^8)/(1-x^16)+16(1-x^8)/(1-x^16)+32/(1+x^16)
=32/(1-x^16)+32/(1+x^16)
=32(1+x^16)/(1-x^32)+32(1-x^16)/(1-x^32)
=64/(1-x^32)