化简：1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+8)(x+9)

分类: 作业答案 • 2021-12-20 01:30:05

问题描述：

答

=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+……+1/(x+8)-1/(x+9)
=1/x-1/(x+9)
=9/x(x+9)

答

化简：
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+8)(x+9)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+8)-1/(x+9)
=1/x-1/(x+9)
=9/x(x+9)