求1×2+2×3+3×4...+n(n+1）的表达式,马上给答案谢谢要原创

求1×2+2×3+3×4...+n(n+1）的表达式,马上给答案谢谢要原创
求1×2+2×3+3×4...+n(n+1）的表达式,马上给答案谢谢
要原创

求1×2+2×3+3×4...+n(n+1）的表达式,马上给答案谢谢要原创
因 n(n+1) = n^2 + n
则
1*2+2*3+3*4.+N*(N+1)
= (1^2 + 2^2 +3^3+.+n^2) +(1+2+3+...+n)
= 1/6n(n+1)(2n+1) + 1/2n(n+1)
= 1/3n(n+1)(n+2)