观察数组(2),(4,6),(8,10,12),(14,16,18,20)...，则第n个括号内各数之和为？
请写过程 谢谢
參考答案:(2)....................2*1
(4,6)..................2*(2 + 3)
(8,10,12)..............2*(4 + 5 + 6)
(14,16,18,20)..........2*(7 + 8 + 9 + 10)
第n项，有n个数字，开始数字为m = n(n-1)/2 + 1
所以，
an = 2*[(2m + n - 1)*n/2]
= (2m + n - 1)*n
= [n(n - 1) + 2 + (n - 1)]*n
= (n^2 + 1)n
检验：
a1 = (1^2 + 1)*1 = 2
a2 = (2^2 + 1)*2 = 10
....