(1/2)数列1n,2(n-1),3(n-2),…,n1的和为（）A.1/6n(n+1)(n+2) B.1/6n(n+1)(2

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(1/2)数列1*n,2(n-1),3(n-2),…,n*1的和为（）A.1/6n(n+1)(n+2) B.1/6n(n+1)(2
(1/2)数列1*n,2(n-1),3(n-2),…,n*1的和为（）A.1/6n(n+1)(n+2) B.1/6n(n+1)(2

(1/2)数列1*n,2(n-1),3(n-2),…,n*1的和为（）A.1/6n(n+1)(n+2) B.1/6n(n+1)(2
n * 1　= n(n+1) - n²
1*n + 2(n-1) + 3(n-2) + ... + n*1
= (1+2+3+...+n)(n+1) - (1² + 2² + 3² + ... + n²)
= n(n+1)(n+1)/2 - n(n+1)(2n+1)/6
= n(n+1)(n+2)/6

这是选择题，直接娶n=1和n=2,，那么很容易就可以选择答案为A，再用n=3验证下就OK了

其实这种选择题考试的时候最好就代数，节省时间。
原式=[1(n+1)-1^2]+[2(n+1)-2^2] + ... +[n(n+1) - n^2]= (1+2+...+n)(n+1) - (1^2 + 2^2 + ... + n^2)= n(n+1)(n+1)/2 - n(n+1)(2n+1)/6= n(n+1)(n+2)/6

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