解方程：1/x(x-1)+1/x(x+1)+1/(x+1)(x+2)+…+1/(x+9)(x+10)=1/12

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/15 19:44:15
解方程：1/x(x-1)+1/x(x+1)+1/(x+1)(x+2)+…+1/(x+9)(x+10)=1/12

解方程：1/x(x-1)+1/x(x+1)+1/(x+1)(x+2)+…+1/(x+9)(x+10)=1/12
解方程：1/x(x-1)+1/x(x+1)+1/(x+1)(x+2)+…+1/(x+9)(x+10)=1/12

解方程：1/x(x-1)+1/x(x+1)+1/(x+1)(x+2)+…+1/(x+9)(x+10)=1/12
1/x(x-1)+1/x(x+1)+1/(x+1)(x+2)+…+1/(x+9)(x+10)
=1/(x-1)-1/x+1/x-1/(x+1)+1/(x+1)-1/(x-2)+.+1/(x+9)-1/(x+10)
=1/(x-1）-1/（x+10)
=11/(x-1)(x+10)=1/12
x^2+9x-142=0
(x+9/2)^2=649/4
x=(-9±√649）/2

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)=1/x-1/(x+1)+1/(x+1)-1/(x+2)+……+1/(x+9)-1/(x+10)=1/x-1/(x+10)=10/(x²+x)

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