How to calculate the simple operation of 1999 × 1999 / 2000

How to calculate the simple operation of 1999 × 1999 / 2000

1999×1999/2000
=(2000-1)x1999/2000
=2000x1999/2000-1999/2000
=1999-1999/2000
=1998 1 / 2000

Given (1 + x) + (1 + x) ^ 2 + (1 + x) ^ 3 +. + (1 + x) ^ n = A0 + a1x + a2x ^ 2 +. Anx ^ n, if a1 + A2 +
Given (1 + x) + (1 + x) ^ 2 + (1 + x) ^ 3 +... + (1 + x) ^ n = A0 + a1x + a2x ^ 2 +... Anx ^ n, if a1 + A2 +... + a (n-1) = 29-n, find n

Let x = 0, then (1 + x) + (1 + x) ^ 2 + (1 + x) ^ 3 +. + (1 + x) ^ n = 1 + 1 ^ 2 +... + 1 ^ n = n
Let A0 = n
Let x = 1, then (1 + x) + (1 + x) ^ 2 + (1 + x) ^ 3 +. + (1 + x) ^ n = 2 + 2 ^ 2 +... + 2 ^ n = 2 ^ (n + 1) - 2
a0+a1x+a2x^2+.anx^n = a0+a1+a2+...+an = 2^(n+1)-2
So A0 + 29-n + a (n) = 2 ^ (n + 1) - 2
We know that a (n) = 1, so n + 29-n + 1 = 2 ^ (n + 1) - 2
32=2^(n+1)
Where are you from?

5-2 7x = 2 37 + 0.4x = 101 6 5-1 = 12 13 9x + x = 25.6 22.5-0.4x = 12.5 3 2x + 4 1x = 33
X-3x = 10.75 × 3-3x = 0.15

5-2 / 7X = 3 / 2
3.5x=3.5
x=1
7+0.4X=101
0.4x=94
x=235
5x-1 in 6 = 13 in 12
5/6x=25/12
x=2.5
9X+X=25.6
10x=25.6
x=2.56
22.5-0.4X=12.5
0.4x=10
x=25
2X / 3 + 1x / 4 = 33
11/12x=33
x=36
X-1 / 3 x = 1 / 6
2/3x=1/6
x=1/4
0.75×3-3X=0.15
2.25-3x=0.15
3x=2.1
x=0.7

A barrel of oil weighs 32 kg. After pouring out 1 / 4, it still weighs 25 kg. How much is the oil weight? How much is the barrel weight?

Hello, Zhang jie'er
Oil weight:
(32-25) △ 1 / 4 = 28 (kg)
Barrel weight:
32-28 = 4 (kg)

Are composite functions y = x ^ 2Sin (1 / x ^ 2) (x is not equal to zero) and y = 0 (x = 0) differentiable?

x> 0, y '= 2xsin (1 / x ^ 2) + x ^ 2cos (1 / x ^ 2) * (- 2 / x ^ 3) = 2xsin (1 / x ^ 2) - 2 / X * cos (1 / x ^ 2)
When X - > 0 +, the above formula has no limit, so it is not differentiable when x = 0

（0.4X+56）/（0.6X-56）=5/4

（0.4X+56）/（0.6X-56）=5/4
（0.4X+56）*4=（0.6X-56）*5
1.6X+224=3X-280
1.4X=504
X=360

In a water pipe with a diameter of 0.8 meters, the water flow rate is 2 meters per second, so how many cubic meters of water flows through the pipe in one minute?

1min = 0.4 × 0.4 × 3.14 × 2 × 60 = 60.288m3

When x → 1, are the three powers of infinitesimal 1-x and 1-x of the same order and equivalent?

The same order is not equivalent

1.8 + 3 and 7 / 15-1 and 9 / 10=

1+4/5+3+7/15-1-9/10
=1+3-1+24/30+14/30-27/30
=3+11/30
=101/30

"Nine chapters of arithmetic" is the earliest existing mathematical monograph in China. It records such a question: "an ancient well, I don't know the depth, a rope is folded three times (Note: folded) and the quantity is more than 2 meters, four fold and the quantity is less than 1 meter." can you calculate the depth of the well? Try it

Let the rope be x meters long
x÷3—2=x÷4+1
x=36
36 △ 3-2 = 10 (m)
A: the well is 10 meters deep