Question

正方形摆放；依次个数是层数+上一层的个数,求n层

Answer 1

1

2+1

3+2+1

4+3+2+1

………………

n+﹙n-1﹚+……+1

n层总数S＝n+2﹙n-1﹚+3﹙n-2﹚+……+n﹙n-n+1﹚

＝﹙1+2+……+n﹚n-[2×1+3×2+4×3+……+n×﹙n-1﹚

注意公式1+2+……+n＝n﹙n+1﹚/2

1×2+2×3+……+n﹙n+1﹚＝n﹙n+1﹚﹙n+2﹚/3

S＝n²﹙n+1﹚/2+n﹙n²-1﹚/3＝﹙n³+3n²-2n﹚/6.