Lim[1/1*2+1/2*3+1/3*4+.+1/n（n+1）]=
lim[(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/n-1/(n-1))]
=lim[1-1/(n-1)]假如n趋于无穷大就等于1