Arrange the natural numbers from small to large, try to find: 1, the sum of the first 10 numbers 2, the sum of the first 100 numbers 3, the sum of the first n numbers

Arrange the natural numbers from small to large, try to find: 1, the sum of the first 10 numbers 2, the sum of the first 100 numbers 3, the sum of the first n numbers

1. The sum of the first 10 numbers: (0 + 9) * 10 / 2 = 9 * 5 = 45
2. Sum of the first 100 numbers: (0 + 99) * 100 / 2 = 9900 / 2 = 4950
3. Sum of the first n numbers: (0 + n) * (n + 1) / 2 = n (n + 1) / 2

There are five natural numbers with the largest number of factors within 100, all of which have 12 factors. The five natural numbers are arranged from large to small, which are 96,90, -?

96,90
84=1*84=2*42=3*28=4*21=6*14=7*12
72=1*72=2*36=3*24=4*18=6*12=8*9
60=1*60=2*30=3*20=4*15=5*12=6*10

First column second column third column fourth column
Line 1 1 4 5 10
Line 2 4 8 10 12
Line 3 9 12 15 14
…… …… …… …… ……
(1) What is the number in the second column of line 10
(2) Where is 81
(3) Where is 100
I might as well look at the answer directly

(1) The second column of 40 is the arithmetic sequence 4 + 4 * (n-1) take n = 10 to get 40 (2) the ninth row. The first column of the first column is the square of the natural number starting from 1. The square of 81 is 9, so in the ninth row, the first column (3) 100 has four positions: 100 is in the tenth row of the first column because it is the square of 10. 100 is referenced in the seventh row of the second column

Do a junior high school mathematics problem regular arrangement
The first column,
The first line is 1,2,5,10,17
Line 2 4, 3611, 18
The third line is 9, 8, 7, 12, 19

The completion point should be such that it can be expanded infinitely
1,2,5,10,17,26,37……
4,3,6,11,18,27,38……
9,8,7,12,19,28,39……
16,15,14,13,20,29,40……
25,24,23,22,21,30,41……
36,35,34,33,32,31,42……
………………………………
Intuitive point of view, you put the number from 1 to the number, you can find the law of arrangement