题目有误,正确答案应该是n(n+1)(n+2)/3(可以代n=1验证)
∑k(k+1)
=∑(k^2+k)
=∑[(k+1)^3-k^3-1]/3
=1/3∑[(k+1)^3-k^3]-∑1/3
=1/3[(2^3-1)+(3^3-2^3)+..+(n+1)^3-n^3]-n/3
=[(n+1)^3-1-n]/3
=n(n+1)(n+2)/3