sn=(n^2+n)/2
s(n-1)=[(n-1)^2+(n-1)]/2
an=sn-s(n-1)
=(n^2+n)/2-[(n-1)^2+(n-1)]/2
=(n^2+n-(n-1)^2-n+1)/2
=n
bn=1/sn
=2/(n^2+n)
=2/n-2/(n+1)