1/2*3*4+1/3*4*5+.+1/8*9*10

设a=1/2*3*4,b=1/3*4*5,c=.g=1/8*9*10
可推出b=a*2/5,c=b*3/6,d=c*4/7,e=d*5/8,f=e*6/9 ,g=f*7/10
a=1/(2*3*4)=1/24
b=1/24*2/5=1/60
c=1/60*3/6=1/120
d=1/120*4/7=1/210
e=1/210*5/8=1/336
f=1/336*6/9=1/504
g=1/504*7/10=1/720
a+b+c+d+e+f+g
=1/24+1/60+c+d+e+f+g=7/120+1/120+d+e+f+g=1/15+1/210+e+f+g
=1/14+1/336+f+g
=25/336+1/504+g=11/144+1/720
=7/90