作业帮1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+...+1/(x+100)(x+101)
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 16:07:25
1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+...+1/(x+100)(x+101)
1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+...+1/(x+100)(x+101)
1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+...+1/(x+100)(x+101)
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+……+1/(x+100)-1/(x+101)
=1/(x+1)-1/(x+101)
=(x+101-x-1)/(x+1)(x+101)
=100/(x+1)(x+101)
答：分式的裂项
1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+...+1/(x+100)(x+101)
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+....+1/(x+100)-1/(x+101)
=1/(x+1)-1/(x+101) (中间各项正负抵消，剩余第一项和最后一项）
=100/[(x+1)(x+101)]
因为1/(x+1)(x+2)=1/x+1 - 1/x+2
同理1/(x+100)x+(101)=1/x+100 - 1/x+101.....
所以原式=1/x+1 - 1/x+2 + 1/x+2 - 1/x+3 +...+ 1/x+100 - 1/x+101 = 1/x+1 - 1/x+101 = 100/(x+1)(x+101)
*-----------------------------------------------*| 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-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
|x-2|+|x-1|