1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+999)(x+1000)

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/03 03:14:27
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+999)(x+1000)

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+999)(x+1000)
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+999)(x+1000)

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+999)(x+1000)
1/x(x+1)=1/x-1/(x+1)
1/(x+1)(x+2)=1/(x+1)-1/(x+2)
...
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+999)(x+1000)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+999)-1/(x+1000)
=1/x-1/(x+1000)=1000/x(x+1000)

原式=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+......+1/(x+999)-1/(x+1000)
=1-1/(x+1000)
=(x+999)/(x+1000)

1/[x(x+1)]+1/[(x+1)(x+2)]+1/[(x+2)(x+3)]+......+1/[(x+999)(x+1000)]
=[1/x-1/(x+1)]+[1/(x+1)-1/(x+2)]+[1/(x+2)-1/(x+3)]+……+[1/(x+999)-1/(x+1000)]
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+……+1/(x+999)-1/(x+1000)
=1/x-1/(x+1000)
=[(x+1000)-x]/[x(x+1000)]
=1000/[x(x+1000)]

*-----------------------------------------------*| 6 4 X | 8 X X | X X 5 || X X X | X X X | X 7 8 || X X X | X X X | X X X ||---------------+---------------+--------------- || X X X | X X X | 5 1 X || X X X | X 6 X | X X X || 8 X X | 3 5 X | 2 X X || 填九宫格帮帮忙.x x 6 x x 7 x x 98 x x x 3 x 1 x x 9 x x 6 x 5 x 3 x x x 3 x x x x 1 8x x x 9 x 1 x x x2 1 x x x x 6 x x x 6 x 7 x 3 x x 1 x x 9 x 2 x x x 47 x x 8 x x 5 x x 七年级下册政治复习提纲(山东人民出版社)第五单元是 青春的脚步 青春的气息别弄错了啊!格式：X X X X X X X X X 1、X X X X X X X X X X.2、X X X X X X X X X.3、X X X X X X X X X X X. 分解因式----（X*X-X)(X*X-X-2)+1 】x(x+1)+x^2(x-1) 1/(1-x)+1/(1+x)+2/(1+x*x)+4/(1+x*x*x*x)+8/(1-x*x*x*x*x*x*x*x)怎么做 x/x+(1-x)/x-1/x x-1/x-2 {2X+1}+{X} (x^2-1)/x x^2-1/x 2X+|X+1| ｜x-1｜+｜x-2｜ (x+1)/(x+2) /X+1/+/X+2/ 2x/(1-x) |X+2|+|X-1| 2x-1 (x