作业帮(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+(-1/4*1/5)+""+(-1/2005*1/2006
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/11/09 04:49:55
(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+(-1/4*1/5)+""+(-1/2005*1/2006)+(-1/2006*1/2007)等于多少?
原式=(-1)×[1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+……+1/(2005×2006)+1/(2006×2007)]
=(-1)×[(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/2005-1/2006)+(1/2006-1/2007)]
=(-1)×(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2005-1/2006+1/2006-1/2007)
=(-1)×(1-1/2007)
=(-1)×2006/2007
= -2006/2007
=(-1)×[(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/2005-1/2006)+(1/2006-1/2007)]
=(-1)×(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2005-1/2006+1/2006-1/2007)
=(-1)×(1-1/2007)
=(-1)×2006/2007
= -2006/2007
(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+(-1/4*1/5)+""+(-1/2005*1/2006
1/1*2+1/3*4+1/4*5+...+1/2004*2005+1/2005*2006,
1/1*2+1/2*3+1/3*4+.+1/2004*2005+1/2005*2006
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2006-1/2005| 的简便算法
2*1 1/2*1 1/3*1 1/4*1 1/5*.1 1/2006*1 1/2007
计算：（1/2+1/3+1/4+…+1//2006）（1+1/2+1/3+…+1/2005）-（1+1/2+1/3+1/
-1+2-3+4+...-2005+2006等于
1/1*2+1/2*3+1/3*4+1/4*5+.+1/2006*2007
(1+1/2+1/3+...+1/2006)*(1/2+1/3+1/4+...1/2007)-(1+1/2+1/3+..
计算:(1/2006-1)(1/2005-1)(1/2004)… (1/3-1)(1/2-1).
计算:(1/2+1/3+...1/2006)(1+1/2+1/3+...1/2005)-(1+1/2+...1/2006
（1）1/2*3+1/3*4+1/4*5.1/2006*2005