(1)/(1+x)+(2)/(1+x^2)+(4)/(1+x^4)+(8)/(1+x^8)+…+(n)/(1+x^n)-(2n)/(1-x^2n)化简

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/05 11:25:47
(1)/(1+x)+(2)/(1+x^2)+(4)/(1+x^4)+(8)/(1+x^8)+…+(n)/(1+x^n)-(2n)/(1-x^2n)化简

(1)/(1+x)+(2)/(1+x^2)+(4)/(1+x^4)+(8)/(1+x^8)+…+(n)/(1+x^n)-(2n)/(1-x^2n)化简
(1)/(1+x)+(2)/(1+x^2)+(4)/(1+x^4)+(8)/(1+x^8)+…+(n)/(1+x^n)-(2n)/(1-x^2n)
化简

(1)/(1+x)+(2)/(1+x^2)+(4)/(1+x^4)+(8)/(1+x^8)+…+(n)/(1+x^n)-(2n)/(1-x^2n)化简
1/(1+x)+2/(1+x^2)+4/(1+x^4)+8/(1+x^8)+…+n/(1+x^n)-2n/(1-x^2n)
=1/(1-x)+1/(1+x)+2/(1+x^2)+4/(1+x^4)+8/(1+x^8)+…+n/(1+x^n)-2n/(1-x^2n)-1/(1-x)
=(1+x+1-x)/(1-x^2)+2/(1+x^2)+4/(1+x^4)+8/(1+x^8)+…+n/(1+x^n)-2n/(1-x^2n)-1/(1-x)
=2/(1-x^2)+2/(1+x^2)+4/(1+x^4)+8/(1+x^8)+…+n/(1+x^n)-2n/(1-x^2n)-1/(1-x)
=4/(1-x^4)+4/(1+x^4)+8/(1+x^8)+…+n/(1+x^n)-2n/(1-x^2n)-1/(1-x)
=8/(1-x^8)+8/(1+x^8)+…+n/(1+x^n)-2n/(1-x^2n)-1/(1-x)
.
=2n/(1-x^2n)-2n/(1-x^2n)-1/(1-x)
=-1/(1-x)
=1/(x-1)