1 1 1 1 ——+——+——+...+—————= 2X4 4X6 6X8 2008X2010 1/2X4 + 1/4X6 + 1/6X8 + ...+ 1/2008X2010

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• 1. 14. In the formula (a + 1) 2 = A2 + 2A + 1, when a takes 1,2,3 , N, we can get the following n equations (1 + 1) 2 = 12 + 2 × 1 + 1 （1+1）2=12+2×1+1 （2+1）2=22+2×2+1 （3+1）2=32+2×3+1 …… （n+1）2=n2+2×n +1 By adding the left and right sides of these n equations, the summation formula can be derived 1+2+3…… +N = (expressed in an algebraic expression containing n)
• 2. In the formula (a + 1) ^ 2 = a ^ 2 + 2A + 1, when a takes 1, 2, 3 respectively N, the following equation can be obtained: (1 + 1) ^ 2 = 1 ^ 2 + 2 * 1 + 1 (2+1)^2=2^2+2*2+1 (3+1)^2=3^2+2*3+1 …… (n+1)^2=n^2+2*n+1 Using the above formulas, conjecture and prove the summation formula, 1 + 2 + 3 + 4 + +n=____ (expressed by the algebraic expression of n)
• 3. What holds in the following equation is the square of () a.a-2a-1 = (A-1) and the square of B.A + A + 1 / 4 = (A-1 / 2) C. Square of B - 6b-9 = (B-3) square C. Square of M + 1 / 6m + 1 / 144 = (M + 1 / 12)
• 4. The first line is 1, the second line is 2, 3, the third line is 4, 5, 6, 7, and the fourth line is 8.9.10.11.12.13.14.15
• 5. What is the integral part of 1 / 2 + 1 / 3 + 1 / 4 + 1 / 5 + 1 / 6 + 1 / 7 + 1 / 8 + 1 / 9 + 1 / 10 + 1 / 11 + 1 / 12? Why
• 6. Observe the equations in the following order: 9 × 0 + 3 = 3, 9 × 1 + 4 = 13 Guess: the nth equation (n is a positive integer) should be expressed as?
• 7. Observe the following equation: 9 × 0 + 1 = 19 × 1 + 2 = 119 × 2 + 3 = 219 × 3 + 4 = 319 × 4 + 5 = 41 According to the law reflected in the number table, we guess that the nth equation (n is a positive integer) should be () A. 9（n-1）+n=10（n-1）+1B. 9n+n=（n-1）+1C. 9n+（n-1）=n2-1D. 9n+n+1=10n+1
• 8. How to easily calculate the square of 1.2222 multiplied by 9-1.3333 multiplied by 4?
• 9. Calculate the square division of - 1 by 1 / 9 times (- 2)
• 10. As shown in Figure 1, ab ∥ CD, try to guess the relationship between ∠ bed and ∠ B, ∠ D? Please explain the reason
• 11. There is a class of numbers, 9-1 = 8,16-4 = 12,25-9 = 16,36-16 = 20. Q n is a positive integer, which is expressed as -?
• 12. Observe the following equations: 9-1 = 8,16-4 = 12,25-9 = 16,36-16-20, ', try the equation about n to express the law you found
• 13. Observe the following equations: 9-1 = 8, 16-4 = 12, 25-9 = 16, 36-16 = 20 Let n be a positive integer. The following equation is () A. （n+2）2-n2=4（n+1）B. （n+1）2-（n-1）2=4nC. （n+2）2-n2=4n+1D. （n+2）2-n2=2（n+1）
• 14. 9-1=8;16-4=12;25-9=16;36-16=20；… What laws do these equations reflect among positive integers
• 15. Observation formula 9-1 = 8; 16-4 = 12; 25-9 = 16; 36-16 = 20 These equations reflect some rules between positive integers, If n is a positive integer, the law can be expressed by the formula of n
• 16. In the following formula, if different Chinese characters represent different numbers, and the same Chinese characters represent the same numbers, then "like math" means "like math" The number of digits is () Love math * learn math = learn math well I'm in a hurry
• 17. For a certain project, if it is contracted by Party A and Party B, it will be completed in two fifths of the day, and the project payment will be 1800 yuan; if it is contracted by Party B and Party C, it will be completed in three fifths of the day, and the project payment will be 1500 yuan; if it is contracted by Party A and Party C, it will be completed in two fifths of the day, and the project payment will be 1600 yuan, And the project payment is the least. Which team should the project be contracted to and how much is the project payment? Team a, B and C contract a project and get a total salary of 21600 yuan. Team a, B and C cooperate for five days to complete one-third of the total project. Team a has six days off, team B has three days off, and team c works until the end. If team a's work efficiency is twice as fast as team C's, and team C's work efficiency is half of team B's, how many yuan should team a, B and C complete the project on the next day? How many of the simplest fractions (coprime of numerator and denominator) are less than 8 and denominator is 24? Party A and Party B contract a project and get a total salary of 1120 yuan. It is known that Party A has worked for 10 days and Party B has worked for 13 days. It is also known that Party A's salary for four days is 40 yuan more than Party B's salary for five days. How much is the salary for Party B? There are 180 workers in workshop a and 120 workers in workshop B of a factory. Now 50 workers are transferred from the two workshops to support the new factory. Due to the increase of workload, the remaining workers are paid 20% more per person per day. Due to different types of work, the workers in workshop a are paid 6 yuan per person per day, while the workers in workshop B are paid 4.8 yuan per person per day, How many workers are there in workshop a?
• 18. As follows: (2a+3b-4c)(2a+3b+4c) =[(2a+3b)-4c][(2a+3b)+4c] =(2a+3b)^2-(4c)^2=4a^2+12ab+9b^2-16c^2
• 19. What is the sum of numbers that can be divided by 9 from 1 to 200
• 20. In the following formula, the divisor can be divided by the divisor A. 12÷0.4B. 1.2÷0.4C. 12÷4