1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)=5/12

来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 18:47:37
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)=5/12

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)=5/12
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)=5/12

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)=5/12
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+9)(x+10)=5/12
1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+9)-1/(x+10)=5/12
1/x-1/(x+10)=5/12
10/x(x+10)=5/12
所以x²+10x-24=0
(x+12)(x-2)=0
x=-12,x=2
经检验,x=-12和x=2是方程的解

原式=1/x-1/(x+10)=5/12
解得：x=2或x=-12


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+2)-1/(x+3)+……+1/(x+9)-1/(x+10)
=1/x-1/(x+10)
=10/x(x+10)
于是
10/x(x+10)=5/12
5x(x+10)=12*10
x²+10x=12*2
x²+10x-24=0
(x-2)(x+12)=0
x-2=0或x+12=0
x=2或x=-12

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