分母的通项是an=1+2+...+n=n(n+1)/2
所以Sn=1/a1+1/a2+...+1/an
=2/1*2+2/2*3+...+2/n(n+1)
=2[(1-1/2)+(1/2-1/3)+...+(1/n-1/(n+1))]
=2[1-1/(n+1)]
=2n/(n+1)