(1/2)^2+(1/3)^2+(1/4)^2+......+(1/n)^2<1*(1/2)+1/2*1/3+1/3*1/4+......+1/(n-1)*1/n=1-1/2+1/2-1/3+1/3-1/4+......+1/(n-1)-1/n=1-1/n<1
