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

One out of two is the first number, one out of six is the second number, and one out of twelve is the third number. It can be found that their molecules are all 1, and denominator 2 can be decomposed into 1 × 2, 6 into 2 × 3, and 12 into 3 × 4, that is, 1 × (1 + 1), 2 × (2 + 1), 3 × (3 + 1) And so on, then the nth numerator is 1

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1. 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
2. 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
3. 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
4. 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)
5. 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
6. 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=______ ×______ ．
7. 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____________________________________ .
8. 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=﹙ ﹚
9. 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
10. 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
11. 1.2.4.7. ().16.22 write the number according to the rule
12. 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
13. 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?
14. 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
15. 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
16. 1/2,1/6,1/12,1/30,1/42…… Find the rule, the nth number is () 1 / 132 is the number
17. 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
18. Formula calculation: 42 is 1 / 6 more than bracket
19. The law calculation of 1 / 12 + 1 / 20 + 1 / 30 + 1 / 42 + 1 / 56
20. Simple calculation 90.909-9.09 + 90.9