简便运算:1/2+1/6+1/12+1/20+1/30+1/42+1/56

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/21 23:00:59
简便运算:1/2+1/6+1/12+1/20+1/30+1/42+1/56简便运算:1/2+1/6+1/12+1/20+1/30+1/42+1/56简便运算:1/2+1/6+1/12+1/20+1/3

简便运算:1/2+1/6+1/12+1/20+1/30+1/42+1/56
简便运算:1/2+1/6+1/12+1/20+1/30+1/42+1/56

简便运算:1/2+1/6+1/12+1/20+1/30+1/42+1/56
1/2+1/6+1/12+1/20+1/30+1/42+1/56
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)
=1-1/8
=7/8
这叫做:裂项相消

列项求和
1/n(n+1)=1/n-1/(n+1)
如1/6=1/2*3=1/2-1/3
故1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1-1/8
=7/8

7/8

1/2+1/6+1/12+1/20+1/30+1/42+1/56=1-1/2+1/2-1/3........+1/7-1/8=7/8

1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1/2×1+1/2×3+1/3×4+1/4×5+1/5×6+1/6×7+1/7×8
=1-1/8
=7/8

1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)=1-1/8=7/8