Is the cycle of "0.9" 9 equal to 1? Why? Ask for detailed process~ O(∩_ Thank you~

Is the cycle of "0.9" 9 equal to 1? Why? Ask for detailed process~ O(∩_ Thank you~

0.99…… =1
Don't know the process, just know the result!
Because this is a college mathematics content, the process is too complicated!
If the method of decimal fraction according to the middle school cycle is simple:
0.99……
=9 out of 9
=1

If the three sides of a triangle are a, B, C and satisfy A4 + B4 + C4 = a2b2 + b2c2 + c2a2, the triangle is equilateral

A 4 + B 4 + C 4 = A 2B 2 + B 2C 2 + C 2A 2, the left and right sides of a 4 + B 4 + C 4 = A 2B 2 + B 2C 2 + C 2A 2 are all × 2, which is written in the form of complete square: (a 2-B 2) 2 + (b 2-C 2) 2 + (C 2-A 2) 2 = 0, ∵ a, B, C are the three sides of a triangle, ∵ a, B, C are nonnegative, ∵ a 2-B 2 = 0, B 2-C 2 =

Five numbers between 1 and 20 add up to 50. What's your formula,

First of all, we need to know the case that the last digit is 0, 1 + 9 = 0,2 + 8 = 0,3 + 7 = 0,4 + 6 = 0,5 + 5 = 0,1 + 1 + 8 = 0,1 + 2 + 7 = 0,1 + 3 + 6 = 0,1 + 4 + 5 = 0,2 + 2 + 6 = 0,2 + 3 + 5 = 0,2 + 4 + 4 = 0,3 + 3 + 4 = 0,1 + 2 + 3 + 4 = 0, then according to the above situation, we can add "1" before the digit and then combine it with 10 or 20

If the solution X and y of the system 4x + 3Y = 1 KX + (k-1) y = 3 are equal, what is the value of K

11

Simple calculation of 9 + 19.9 + 199.9 + 1999.9 + 19999.9

9+19.9+199.9+1999.9+19999.9
=10-1+20-0.1+200-0.1+2000-0.1+20000-0.1
=10+20+200+2000+20000-1-0.1-0.1-0.1-0.1
=22230-1.4
=22228.6

We know a series of numbers: 1,3 / 4,5 / 9,7 / 16,9 / 25. The nth number is, and the 100th number is

The nth number is 2N-1 / N * n, and the 100th number is 199 / 10000

[49 / 12-63 / 20 + 77 / 30-91 / 42 + 105 / 56) - 3 and 1 / 6] △ 1 / 24 simple calculation process, / is the fractional line, △ is the fractional line
[(49 / 12-63 / 20 + 77 / 30-91 / 42 + 105 / 56) - 3 and 1 / 6] / 1 / 24
Simple calculation process, / is the fraction line, △ is the division sign

Original formula = (3430 / 840-2640 / 840 + 2156 / 830-1820 / 840 + 1575 / 840-2660 / 840) * 24
=41/840*24
=41/35

The bottom of a triangle is 14cm. If the bottom is increased by 2cm, the area will be increased by 2cm. What is the original area of the triangle

Because the bottom of a triangle is 14 cm. If the bottom is increased by 2 cm, the area will be increased by 2 square cm. The area = half of the height of the bottom * so the height is 2, so the original area = 2 * 14 / 2 = 14

Solution equation: (18-2x) (12-x) = 196

(18-2x)(12-x)=196
216-18x-24x+2x^2-196=0
2x^2-42x+20=0
x^2-21x+10=0
x=(21±√(441-40))/2
=(21±√401)/2

There is a semicircular piece of paper with a circumference of 10.28 cm. What is the area of this piece of paper
The circumference of a semicircle paper is 10.28 decimeters. How many square meters is its area?
The result of my calculation is:
10.28*2=20.56dm
20.56 / 2 / 3.14 = 3.27388535
It is conceivable that it is wrong to seek a positive solution

πr+2r=10.28
r=10.28/(2+π)
s=πr²/2=π*10.28²/(2+π)² /2
=12.56 /2
=6.28 square decimeters