1^2+2^2+3^2+……+n^2=(1^2+1)+(2^2+2)+(3^2+3)+……+(n^2+n)-n(n+1)/2=2[(2*1)/2+(3*2)/2+(4*3)/2+……+n*(n+1)/2]-n(n+1)/2=2(C22+C32+C42+……+C(n+1)2)-n(n+1)/2,(C22表式C2选2,C32表式C3选2……)=2(C33+C32+C42+……+C(n+1)2))-n(n+1)/2=2C(n+2)3)-n(n+1)/2,(C33+C32=C43,C43+C42=C53……)=(n+1)n(n-1)/3-n(n+1)/2=[2(n+2)(n+1)n-3n(n+1)]/6=n(n+1)(2n+1)/6此方法用到高三组合数公式