1，go: A0
Step 1: A 1=A0+ 1.
Step 2: A2=A0+ 1-2.
Step 3: A3=A0+ 1-2+3.
Step 4: A4=A0+ 1-2+3-4.
…… :……
Step 50: A50 = A0+1-2+3-4+…+47-48+49-50.
Let's start sorting out these data. a50 = A0+ 1-2+3-4+…+47-48+49-50 = A0+( 1-2)+(3-4)+…+(47-48)+(49-49)。
2,(-2)^2005+(-2)^2006=(-2)^2005x(-2+ 1)=-2^2005x(- 1)=2^2005；
3,2-22-23 ...-218-219+220, the real question is obviously a question of finding regularity. First, we can match the original formula = 4-2-2-2 3...-2 65438.
-2-2^2=-6=-2^3+2; -2-2^2-2^3=- 14=-2^4+2; -2-2^2-2^3-2^4=-2^5+2,……,
-2-22-23-24-...-218-219 =-220+2, so the original formula = 4-220+220 = 6;
4. First, change 4 and 65438+9 of 06 into false scores, and 4 and 65438+9 of 06 = (4 *16+9)/16 = 73/16, so that we can get:
√(4 and 65438+9/06) = √ (73/16) = √ 73/4;
5. 1/2, 1/3,110,115, 1/26,1/36 1/(3 2+ 1), 1/(4 2- 1), 1/(5 2+ 1), 1/(6
6. x-5y=0, then x=5y. If you substitute (3x+6y)/(2x-3y), you get: (15y+6y)/10y-3y = 3;
7. If a=-b with a+b=0 is substituted into a3 +a2b-ab2-b3, we can get: (-B) 3+(-B) 2B-(-B) B2-B3 =-B3+B3-B.
8. According to the complete square formula: (x2-8x+ 16)=(x-4)2, (9-6x+x2) =(3-x)2, so √(x2-8x+ 16)+√(9-6x+x2).
9, this question is a bit like a discussion question, a bit difficult. If there are x dormitories, the number of students is (8x+ 12). If there are 9 people living in each room, there are two rooms. This sentence means that (x-3) rooms are full, (x-2) rooms may or may not be full, and the remaining two rooms are empty, so it can be counted continuously.
Room X-2 1 person: 8x+ 12=9(x-3)+ 1, and the total number of boarders is 316;
There are two people in Room X-2: 8x+ 12=9(x-3)+2, x=37, and the total number of boarders is 308;
Room X-2 has 3 people: 8x+ 12=9(x-3)+3, x=36, and the total number of boarders is 300;
Room X-2 has 4 people: 8x+ 12=9(x-3)+4, x=35, and the total number of boarders is 292;
Room X-2 has 5 people: 8x+ 12=9(x-3)+5, x=34, and the total number of boarders is 284;
Room X-2 has 6 people: 8x+ 12=9(x-3)+6, x=33, and the total number of boarders is 276;
Room X-2 has 7 people: 8x+ 12=9(x-3)+7, x=32, and the total number of boarders is 268;
When there are 8 people in Room X-2: 8x+ 12=9(x-3)+8, x=3 1, and the total number of boarders is 260;
Therefore, you can refer to the above answer;
10, assuming that the cost is a yuan and the price is b yuan, there is a formula: (b-a)/a = m% ... (1), so when the cost is reduced by 8%, there is: (b-92% a)/92% a = (m+6544.
1 1, the key to this problem is to understand the definition of linear equation with one variable. The definition is: an equation has an unknown number, and the number of times to cut the unknown number is 1, which is called a linear equation. According to the definition, (∣ a ∣-1) x2+(a- 1) x4 b-3 = 0, ∣ a-1= 0, a-1.
a2-2ab+b2=(a-b)^2=(- 1- 1/4)^2=25/ 16；
12, 1+2-3+4-5 …-99+ 100 = 1+(2-3)+(4-5) …+(98-99)+ 100.
To sum up, the key to dealing with mathematical problems is to have enough confidence and patience, and pay attention to absorbing the definitions in books. All mathematical problems are based on definitions, and many problems are extensions of basic definitions. We'll talk later!