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

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• 1. 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=______ ×______ ．
• 2. 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____________________________________ .
• 3. 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=﹙ ﹚
• 4. 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
• 5. 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
• 6. 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
• 7. 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
• 8. What rules can you find by observing the following formulas? 1*3+1=4=2^2 2*4+1=9=3^2 3*5+1=25=5^2. (1) Please write two more equations according to your observation (2) According to the same number equation, please put the rules you find out in letters
• 9. Please observe the following formulas carefully, and then write the fourth and fifth formulas according to the rules you found √16=√1x16=√1x4²=√1x√4²=1x4=42.√32=√2x16=√2x4²=√2x√4²=√2x4=4√23.√48=√3x16=√3x4²=√3x√4²=√3x4=4√34.√64=__________________ 5.√80=_____________________ Please write the nth equation that agrees with the above rule. (n ≥ 1, and it is an integer)
• 10. Mathematics (4th power of a) + 6th power of a * 2nd power of a
• 11. 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)
• 12. 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
• 13. 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
• 14. 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
• 15. 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
• 16. 1.2.4.7. ().16.22 write the number according to the rule
• 17. 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
• 18. 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?
• 19. 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
• 20. 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