由题意知：
设第n个数为an
则：a1=(1/2)-[1-(1/2)]
a2=(1/3)-[1-(1/2)][1-(2/3)]
a3=(1/4)-[1-(1/2)][1-(2/3)][1-(3/4)]
.
an=[1/(n+1)]-[1-(1/2)][1-(2/3)][1-(3/4)].{1-[n/(n+1)]}
=[1/(n+1)]-[1/(2*3*4*5*6*.*n*(n+1)]
=[1/(n+1)]*{1-[1/(2*3*4*5*.*n)]}
=[1/(n+1)]*[1-(1/n!)]
=(n!-1)/(n+1)!

所以：
a10=(10!-1)/11!=3628799/39916800=0.090909065856983
a11=(11!-1)/12!=39916799/479001600=0.083333331245658
a12=(12!-1)/13!=479001599/6227020800=0.076923076762486
a13=(13!-1)/14!=6227020799/87178291200=0.071428571417101

最大的数为a10,即：第十个数最大