初一拓展思维数学题

1/(1*3)=1/2*(1-1/3)
1/(2*4)=1/2*(1/2-1/4)
1/(3*5)=1/2*(1/3-1/5)
.....
1/(17*19)=1/2*(1/17-1/19)
1/(18*20)=1/2*(1/18-1/20)

原式
=1/2*[(1-1/3)+(1/2-1/4)+...+(1/17-1/19)+(1/18-1/20)]
=1/2*(1+1/2-1/3+1/3-1/4+...+1/17+1/18-1/19-1/10)
=1/2*(1+1/2-1/19-1/20)
=1/2*531/380
=531/760

因为d/n*（n+d）=1/n - 1/（n+d)
比如2/1*（1+2）=1-1/3
又比如2/3*（3+2）=1/3-1/5
但这道题里分子不是2而是1，所以要把原式先乘以2，再除以2
解：原式=[1/1*3+1/2*4+1/3*5+1/4*6.....+1/18*20]*2/2
=[2/1*3+2/2*4+2/3*5+1/4*6.....+2/18*20]/2
=[1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+.....+1/18-1/20]/2
=[1-1/19+1/2-1/20]/2
=(18/19+9/20)/2
=9/19+9/40
=531/760

-5+21*8/2-6-59
68/21-8-11*8+61
-2/9-7/9-56
4.6-(-3/4+1.6-4-3/4)
1/2+3+5/6-7/12
[2/3-4-1/4*(-0.4)]/1/3+2
22+(-4)+(-2)+4*3
-2*8-8*1/2+8/1/8
(2/3+1/2)/(-1/12)*(-12)
(-28)/(-6+4)+(-1)
2/(-2)+0/7-(-8)*(-2)