1. Given x-3y = 0, find the value of (2x + y) of (x's Square - 2XY + Y's Square) 2. Given that (1 / b) - (1 / a) = 1, find the value of (2a + 3ab-2b) of (a-2ab-b)

1. Given x-3y = 0, find the value of (2x + y) of (x's Square - 2XY + Y's Square) 2. Given that (1 / b) - (1 / a) = 1, find the value of (2a + 3ab-2b) of (a-2ab-b)

（1）7/4y
(2)-5

1. Group A and group B went to the nursing home 4.5km away from the school to clean up. Half an hour after group a started walking, group B started to set out by bike. As a result, the two groups arrived at the nursing home at the same time. If the walking speed of group A was 1 / 3 of that of group B, what was the walking speed of group A and that of group B
2. The buyer of Hualian Shopping Mall found a kind of emergency shirt in Suzhou, which was expected to sell well. He bought all the shirts with 80000 yuan, but he needed two times more. After being introduced, he bought the needed shirts with 176000 yuan in Shanghai, but the unit price was 4 yuan higher than that in Suzhou. The shopping mall sold them at 58 yuan per piece, which sold well. Finally, only 150 of them were sold at 20% discount, It will be sold out soon. How much is the profit of this business?

Solution 1: the walking speed of group A is x km / h, then the cycling speed of group B is 3x km / h; the walking time of group A is 4.5/x hours, and the cycling time of group B is 4.5 / (3x) hours; according to the half-hour more time of group A than group B, the equation is: 4.5 /

A fraction question for the second semester of the eighth grade
If 1 / A-1 / b = 5, what is the value of fraction (2a-ab-2b) / (AB-A + b)?

Because (B-A) / AB = 5, B-A = 5ab, so 2a-ab-2b) / (AB-A + b) = (2 * (a-b) - AB) / (ab - (a-b)) = (- 10ab AB) / (AB + 5ab) = - 11 / 6

1x2x3 = 6 3x4x5 = 60 5x6x7 = 210 2x3x4 = 24 4x5x6 = 120 the product of three continuous natural numbers (except 0) must be a multiple of which number and why

2 and 3
Because at least one of the three continuous natural numbers is even and greater than or equal to 2, their product must be a multiple of 2
Three continuous natural numbers have a multiple of 3, so their product must be a multiple of 3

1x2x3+2x3x4+3x4x5+4x5x6+...+n(n+1)(n+2)=

The original formula is 1 / 4 (- 0 * 1 * 2 * 3 + 1 * 2 * 3 * 4) + 1 / 4 (- 1 * 2 * 3 * 4 + 2 * 3 * 4 * 5) + +1/4[-（n-1)n(n+1)(n+2)+n(n+1)(n+2)(n+3)]
=1/4[-0*1*2*3*4+n(n+1)(n+2)(n+3)]
=n(n+1)(n+2)(n+3)/4

1x2x3+2x3x4+3x4x5+.+7x8x9=?
1x2=1/3(1x2x3-0x1x2)
2x3=1/3(2x3x4-1x2x3)
3x4=1/3(3x4x5-2x3x4)
1x2+2x3+3x4=1/3x3x4x5=20

In general, there are:
(n-1)n(n+1)
=n^3-n
The sum formula of {n ^ 3}: SN = [n (n + 1) / 2] ^ 2
{n} Sum formula: SN = n (n + 1) / 2
1x2x3+2x3x4+3x4x5+.+7x8x9
=2^3-2+3^3-3+...+8^3-8
=(2^3+3^3+...+8^3)-(2+3+...+8)
=[(8*9/2)^2-1]-8*9/2+1
=1260

1x2x3+2x3x4+3x4x5+.+10x11x12

Let n be an
an=n(n+1)(n+2)=n^3+3n^2+2n
1×2×3+2×3×4+...+10×11×12
=(1^3+2^3+...+10^3)+3(1^2+2^2+...+10^2)+2(1+2+...+10)
=[10(10+1)/2]^2+3×10×(10+1)(20+1)/6+2×10×11/2
=3025+1155+110
=4290
Formula used:
1^3+2^3+...+n^3=[n(n+1)/2]^2
1^2+2^2+...+n^2=n(n+1)(2n+1)/6
1+2+3+...+n=n(n+1)/2

1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+.1/(20x21x22)=?

1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+.1/(20*21*22) =1/2[1/1*2-1/2*3]+1/2[1/2*3-1/3*4]+1/2[1/3*4-1/4*5]+...+1/2[1/20*21-1/21*22] =1/2[1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+...+1/20*21-1/21*22] =1/2[1/2-1/21*22]...

1/1x2x3+1/2x3x4+1/3x4x5+------+1/98x99x100=

1/1x2x3+1/2x3x4+1/3x4x5+------+1/98x99x100
=(1/2)*(1/1*2-1/2*3)+(1/2)*(1/2*3-1/3*4)+...+(1/2)(1/98*99-1/99*100)
=(1/2)*(1/1*2-1/2*2+1/2*3-1/3*4+...+1/98*99-1/99*100)
=(1/2)*(1/2-1/9900)
=(1/2)*(4949/9900)
=4949/19800.

1/1x2x3+1/2x3x4+1/3x4x5+.+1/9x10x11=

1/n(n+1)(n+2)=1/2*[1/n-2/(n+1)+1/(n+2)]
Original formula = 1 / 2 * (1-2 * 1 / 2 + 1 / 3 + 1 / 2-2 * 1 / 3 + 1 / 4 +. + 1 / 9-2 * 1 / 10 + 1 / 11)
=1/2*(1-1/2-1/10+1/11)=27/110