不知道你学过“阶乘”没有?!1×2×3×……×(n-1)×n=n!按照题目所给的提示,分母分别为(n+1)!这样,各项就是n/(n+1)!=[(n+1)-1]/(n+1)!=[(n+1)/(n+1)!]-[1/(n+1)!]=(1/n!)-[1/(n+1)!]所以,原式=[1-(1/2!)]+[(1/2!)-(1/3!)]+……[(1/5!)-(1/6!)]=1-(1/6!)=1-(1/1×2×3×4×5×6)=719/720