1/N(N+I)+1/(N+1)(N+2)+1/(N+2)(N+3)+.+1/(N+9)(N+10)
=1/n-1/(n+1)-1/(n+1)-1/(n+2)+1/(n+2)-1/(n+3)+---+1/(n+9)-1/(n+10)
=1/n-1/(n+10)
=10/[n(n+10)]
=10/(n²+10n)