请问 1^2+2^2+3^2+……+n^2=n(n+1)(2n+1)/6 如何证明呢？我已冥思苦想

1^2+2^2+3^2+……+n^2 =1*2-1+2*3-2+3*4-3+……+n(n+1)-n =(1*2+2*3+3*4+……+n(n+1))-(1+2+3+……+n) =n(n+1)(n+2)/3-n(n+1)/2 =n(n+1)(2n+1)/6