1.简便计算1/21/31/41/51/6
1. 简便计算 1/2 1/3 1/4 1/5 1/6 -
1/2+1/3+1/4+1/5+1/6 =(1/2+1/3+1/6)+1/4+1/5 =1+1/4+1/5 =29/20
=1/2+1/6+1/12+1/20 =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5 =1-1/5 =4/5
1/2+1/3+1/4+1/5+1/6 =(1/2+1/3+1/6)+1/4+1/5 =1+1/4+1/5 =29/20
=1/2+1/6+1/12+1/20 =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5 =1-1/5 =4/5
原式=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7 =1/2-1/7 =5/14.
1/3+1/4+1/6 =4/12+3/12+2/12 =9/12 =3/4
...1、20分之1、30分之1、42分之1、56分之1(简便方法计算) -
1/6=1/2-1/3 1/12=1/3-1/4 1/20=1/4-1/5 1/30=1/5-1/6 希望你能满意。规律就是前一项的减数就是后一项的加数，因此可以得到下面这个算法：1/2+1/6+1/12+1/20+1/30+1/42+1/56 =1/(1*2)+1/(2*3)+1/(3*4)+..+1/(7*8)=(1-1/2)+(1/2-1/3)+(1/3-1/4)+希望你能满意。.
(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）展开消掉=1-1/8=7/8
21/5*1/31+4/5*21/31简便计算 -
21/5×1/31＋4/5×21/31 ＝21÷(5×31)＋(4×21)÷(5×31)＝(21＋4×21)÷(5×31)＝(5×21)÷(5×31)＝5×21÷5÷31 ＝21÷31 ＝21/31
釆用裂项求和法简算：1/6+1/12+1/20+1/30+1/42 =1/（2×3）1/（3×4）1/（4×5）1/（5×6）1/（6×7）1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7 =1/2-1/7 =5/14
在计算1/8+1/6+51/6应用什么律使计算简便 -
1/8+1/6+51/6 =1/8+(1/6+51/6)应用加法结合律使计算简便，
1/2=1-(1/2)1/6=(1/2)(-1/3)1/12=(1/3)-(1/4)……1/110=（1/10）（1/11）所以结果为：1-(1/2)+(1/2)-(1/3)+(1/4)-(1/5)+……(1/10)-(1/11)=1-（1/11）10/11