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

来源:学生作业学帮网 编辑:学帮网 时间:2024/05/14 19:55:28

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

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)

=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)