正整数按下列方法分组:{1},{2,3,4},{5,6,7,8,9},{10,11,12,13,14,15,16},…记第n组中各

2024-08-16 01:10:18
推荐回答(1个)
回答1:

{1},宽缓渗{2,3,4},{5,6,7,8,9},{10,11,12,13,14,15,16},…
前n组共有1+3+5+…+(2n-1)=n2个正整数,故
An=(1+2+3+…+n2)-[1+2+3+…慎脊+(n-1)2]
(哪肆用前n组的和减去前n-1组的和)
=

n2(1+n2)
2
-
(n?1)2[1+(n?1)2]
2

=(2n-1)(n2-n+1)
Bn=n3-(n-1)3
故An+Bn=2n3
故答案为:2n3