1=1+n-n=n+1-n=（n+1）-n1/(n(n+1))=(（n+1）-n)/(n(n+1))=（n+1）/(n(n+1)) - n/(n(n+1))=1/n - 1/(n+1)1/n(n+1)=1/n-1/(n+1)所以前n项和为1-1/2+1/2-1/3+1/3+...+1/n-1/(1+n)=1-1/(1+n)
