1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+1998)(x+1999),当x=1时,求该代数式的值

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/19 21:36:40
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+1998)(x+1999),当x=1时,求该代数式的值1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+1998)(x+1999),当x=1时,求该代数式的值
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+1998)(x+1999),当x=1时,求该代数式的值

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+1998)(x+1999),当x=1时,求该代数式的值
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+1998)(x+1999)
=[1/x-1/(x+1)]+[1/(x+1)-1/(x+2)]+[1/(x+2)-1/(x+3)]+.+[1/(x+1998)-1/(x+1999)]
=1-1/(x+1999)
=1-1/2000
=1999/2000