Sn=n(n+1)(2n+1)/6用阶差法求:(n+1)^3=n^3+3n^2+3n+1n^3=(n-1)^3+3(n-1)^2+3(n-1)+1(n-1)^3=(n-2)^3+3(n-2)^2+3(n-2)+1……2^3=1^3+3*1^2+3*1+11^3=0^3+3*0^2+3*0+1将上式累加,可得(n+1)^3=3*Sn+3*(1+2+3+……+n)+n+1可得Sn=n(n+1)(2n+1)/6