Sn=(2^2)/(1×3)+（4^2)/(3×5)+.((2n)^2)/(2n-1)(2n+1)=(1+1/(1*3))+(1+1/(3*5))+.(1+1/(2n-1)(2n+1))=n+(1/1*3+1/3*5+.1/(2n-1)(2n+1))=n+(1/2)(1-1/(2n+1))=n+n/(2n+1)=(2n^2+2n)/(2n+1)