因为1/1+2=1-1/2 1/2+3=1/2-1/3 1/3+4=1/3-1/4 1/n+n+1=1/n-1/n+1
所以得(1/1+2)+(1/2+3)+(1/3+4)+.+(1/n+(n+1))=1-1/2+1/2-1/3+1/3-1/4+.+1/n-1/n+1
=1-1/(n+1)=n/(n+1)