One column number: 0, - 1, 3, - 6, 10, - 15, 21 According to this rule, the nth number is______ ．

One column number: 0, - 1, 3, - 6, 10, - 15, 21 According to this rule, the nth number is______ ．

The nth number is 0 + 1 + 2 + 3 + +(n-1) = n (n − 1) 2, the sign is (- 1) n-1, so the nth number is (- 1) n-1n (n − 1) 2

Ancient Greek mathematicians put 1,3,6,10,15,21 It's called triangle number. According to its law, the difference between the 24th and the 22nd

①1=1,②3=1＋2,③6=1＋2＋3,④10=1＋2＋3＋4,…… The nth number = 1 + 2 + 3 + The difference between the 24th number and the 22nd number is 47

Put 1, 3, 6, 10, 15, 21 It's called the number of triangles. If it has a certain rule, what's the difference between the number of the 24th triangle and the number of the 22nd triangle?

Sn=n(n+1)/2
S24=24*25/2=300
S22=22*23/2=253
S24-S22=47
Or directly
S23-S22=23
S24-S23=24
S24-S22=23+24=47

Fill in 24, 20, 12, 21, 6, 22 () and () according to the rule

Law of odd terms: each number is half of the previous one; law of even terms: each number is 1 larger than the previous one
So: 24, 20, 12, 21, 6, 22 (3), (23), 1.5

Ancient Greek mathematicians called numbers 1,3,6,10,15,21,... Trigonometric numbers. If they have certain rules, the difference between the 24th trigonometric number and the 22nd trigonometric number is

1
2, 3
4, 5, 6
7, 8, 9,10
11,12,13,14,15
……
The last number of each row is the trigonometric number, and the difference between it and the last one is the number of rows n,
The 22nd number is 1 + 2 + 3 + +22
The 24th number is 1 + 2 + 3 + +22+23+24
Subtract two lines, the 24th number is more than the 22nd number, 23 + 24 = 47

Fill in six numbers 1.2.3.4.5.6 in your mouth, and each number is used only once. Mouth ten = mouth ten = mouth ten. Fill in eight numbers 0.1.2.3.4.5.6.7 in your mouth, and each number is used only once

1+6=2+5=3+4

Fill in six numbers 123456 in the box, each number is only used once, mouth ten = mouth ten = mouth ten

1、6、2、5、3、4

1 / 2, 1 / 3, 1 / 10, 1 / 15, 1 / 26, 1 / 35. Write the seventh number in order

One in 50
Square of ordinal number + 1 (when ordinal number is odd)
-1 (even ordinal)

Simplify 2 (a + 1) - 1

=2A + 1 thank you

a(1_ a)+(a+1)2_ Simplification 1

a(1_ a)+(a+1)2_1
=a-a^2+a^2+2a+1+1
=3a+2