1）1/1×6+1/6×11+1/11×16+1/16×21

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/10/03 03:44:32

1）1/1×6+1/6×11+1/11×16+1/16×21
2）1/8+1/24+1/48+1/80+1/120
3)(1/2+1/3+1/2004)(1+1/2+.+1/2003)-(1+1/2+.1/2014)(1/2+1/3+.+1/2003)

1）1/1×6+1/6×11+1/11×16+1/16×21
=1/5(5/1×6+5/6×11+5/11×16+5/16×21)
=1/5×(1-1/6+1/6-1/11+1/11-1/16+1/16-1/21)
=1/5×(1-1/21)
=1/5×20/21
=4/21
2）1/8+1/24+1/48+1/80+1/120
=1/4(1/2+1/6+1/12+1/20+1/50)
=1/4(1/1×2+1/2×3+1/3×4+1/4×5+1/5×6)
=1/4×(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6)
=1/4×(1-1/6)
=5/24
3)(1/2+1/3+……+1/2004)(1+1/2+.+1/2003)-(1+1/2+.1/2014)(1/2+1/3+.+1/2003)
设1/2+1/3+.+1/2003=a
则原代数式可化为
(a+1/2014)(1+a)-(1+a+1/2014)a
=a+a²+1/2014+a/2014-a-a²-a/2014
=1/2014

计算1/1*6+1/6*11+1/11*16+1/16*21+.+1/51*56 1 /6×11+1/11×16+1/16×21+1/21×26+1/26×31+1/31×36 = 计算1/（6*11）+1/（11*16）+1/（16*21）+1/（21*26）+1/（26*31）+1/（31*36）简便方法运算用简便方法运算.1/1*6+1/6*11+1/11*16+1/16*21 1/6+1/12+1/20+1/3 1/1*6 +1/6*11+ 1/11*16+ 1/16*21+ 1/21*26+1/26*31+...+1/51*56 找规律:1,6,11,16,21,26. 1*6分子1+6*11分之1+11*16分之1+.+101*106分之1 1/1*6+1/6*11+1/11*16+.+1/51*56如何巧算? 用简便方法计算：1/1*6+1/6*11+1/11*16+...+1/101*106 1/1×6+1/6×11+1/11×16+------+1/101×106如何简便计算 1/6+1/6*11+1/11*16+.+1/2006*2011=? 5/2+9/4-5/1+9/1 15/3+6/5+15/2 11/5+2/1-11/4 21/16-16/3-16/1