l×l＋2×2＋…＋n×n＝?为什么

l×l＋2×2＋…＋n×n=1^2+2^2+…+n^n=n(1/6)(n+1)(2n+1)
证明:
∑r^2
=∑(r^2-r+r)
=∑[(r-1)r+r]
=∑(r-1)r+∑r
=∑r(r+1)+∑r<∑r(r+1)的∑上面是n-1,其他的都是n>
=[∑r(r+1)-n(n+1)+(1/2)n(n+1)
=(1/3)n(n+1)(n+2)-(1/2)n(n+1)
=(1/6)n(n+1)[2(n+2)-3]
=n(1/6)(n+1)(2n+1)

n*(n+1)*(2n+1）/6
公式