32-12=8×1;52-32=8×2;72-52=8×3… Observe the above formula, what law can you find? Please use algebra to express, and use this law to calculate the value of 20012-19992
Is (2n + 1) 178; - (2n-1) 178; = 8N
2001=2×1000+1
So n = 1000
So the original formula = 8 × 1000 = 8000
RELATED INFORMATIONS
- 1. Carefully observe the rules of the following group of formulas and write two such formulas: 99-27 = 72, 88-35 = 53, 77-25 = 52, 55-23 = 32
- 2. Observe the following three groups of formulas, find the rules and fill in the blanks 1 × 2 = 2 × 3 of 3, 1 × 2 + 2 × 3 = 2 × 3 × 4 of 3, 1 × 2 + 2 × 3 + 3 × 4 = 3 × 4 × 5 of 3 (1) 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 = 4 × 5 × () (2) 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + 5 × 6 = () × () × () (3)1×2+2×3+3×4+… +N × (n + 1) = () × () × () (4) 1 × (1 × 2 + 2 × 3 + 3 × 4 +) + 199 × 200) = (this one needs to be written)
- 3. Observe each of the following formulas and fill in the blanks according to the rules you find 4*5=20,3*6=18 5*6=30,4*7=28 6*7=42,5*8=40 . If 1222 * 1223 = 1494506, then 1221 * 1224 = () Write the relationship
- 4. 2 + 4 = 2 × 3 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 2 + 4 + 6 = 3 × 42 + 4 + 6 + 8 = 4 × 5 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 2 + 4 + 6 + 8 + 10 + +100=______ ×______ .
- 5. First observe the following formula, fill in the blanks and summarize the rules 3²-1²=8×1, 5²-3²=8×2; Then (1) 7 & sup2; - 5 & sup2; = 8 × (3) (2)9²-(7)²=8×4 (3)(11)²-9²=8×5 Sum up the law____________________________________ .
- 6. Observe the following formula and fill in the blanks 1.07÷9=0.118 1111.04÷9=﹙ ﹚ 11.06÷91.228 ﹙ ﹚÷9=﹙ ﹚ 111.05÷9=12.338 ﹙ ﹚÷9=﹙ ﹚
- 7. Looking at the following formulas, what rules do you find? ①16×14=224=1×(1+1)×100+6×4 ②23×27=621=2×(2+1)×100+3×7 ③32×38=1216=3×(3+1)×100+2×8 Simple description of the above found rules: mainly text and letters
- 8. Observe the following formulas: 31 = 3 & nbsp; & nbsp; & nbsp; 32 = 9 & nbsp; & nbsp; & nbsp; & nbsp; 33 = 27 & nbsp; & nbsp; & nbsp; & nbsp; 34 = 81 & nbsp; & nbsp; & nbsp; & nbsp; 35 = 243 & nbsp; & nbsp; & nbsp; & nbsp; 36 = 729 & nbsp; & nbsp; & nbsp; 37 = 2187 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 38 = 6561 Use the rule you found to judge the last number of 32004 is () A. 3B. 9C. 7D. 1
- 9. What rules do you find by observing the following formulas 1^2=(1×2×3)/6 1^2+2^2=(2×3×5)/6 1^2+2^2+3^2=(3×4×5)/6 1^2+2^2+3^2+4^2=(4×5×9)/6 … (1) Can you express this rule with a formula? (2) According to the rule you found, calculate 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + +8^2 Second, the process
- 10. If you look at the following formula, you will find the rule The second power of 1-0 = 1; the second power of 2-1 = 3; the second power of 3-2 = 5; the second power of 4-3 = 7; the second power of 5-4 = 9
- 11. Observe the following equations, find the laws from them, and use them to find the values of the following equations Look at the following equations: 1/√2+1=√2-1,1/√3-√2,1/√4-√3,1/√5+√4=√5-√4,… Find the laws from the above equations and use them to find the values of the following equations 1/√2+1+1/√3+√2+1/√4+√3+…… +1/√2013+√2012
- 12. Observe this series of regular numbers: 1 / 2, 1 / 6, 1 / 12, 1 / 30, 1 / 42, and know what the nth number is according to the law
- 13. 1.2.4.7. ().16.22 write the number according to the rule
- 14. A column of numbers 0, negative 2,6, negative 12,20, negative 30,42, etc. write the eighth number and the nth number according to this rule Ask for answers
- 15. Observe the following regular numbers: 1 / 2, 1 / 6, 1 / 12, 1 / 20, 1 / 30, 1 / 42... What is the seventh? 1 / 380? What is the nth?
- 16. Observe the following regular numbers: 1 / 2, 1 / 6, 1 / 12, 1 / 20, 1 / 30, 1 / 42... Write the seventh and N numbers according to the law
- 17. Observe the following list of regular numbers: 1 / 2, 1 / 6, 1 / 12, 1 / 30, 1 / 42 (2) 1 / 272 is the number one in the column_ individual (3) Calculate the sum of the first 20 numbers
- 18. 1/2,1/6,1/12,1/30,1/42…… Find the rule, the nth number is () 1 / 132 is the number
- 19. 1 / 2, 1 / 6, 1 / 12, 1 / 20, 1 / 30, 1 / 42. According to the law, the seventh number is. The nth number is. 1 / 132 is the number
- 20. Formula calculation: 42 is 1 / 6 more than bracket