50-49+48-47+46-… +4-3 + 2-1, simple algorithm

（50-49） +（48-47）+.+（2-1）=25X1=25

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1. Fill in the blanks in the first day of junior high school! 1×2=1／3×1×2×3,1×2+2×3=1／3×2×3×4,1×2+2×3+3×4+4×5 =1／3×4×5×6,... According to the above rule, please guess: 1 × 2 + 2 × 3 + 3 × 4 +... + n (n + 1) (n is an integer)=------------- Very urgent ah, help, the right answer plus 50 points ah, speed!
2. There is a column of numbers as follows: 4, 5, 9, 14, 23. What is the number 1999?
3. There is a column of numbers, 2, 5, 8, 11, 14 Then 104 is the () th number in this column A. 33B. 32C. 34D. 35
4. 1.1.2.3.5.8.13.21.34. According to the characteristics of this column, what are the two numbers after the 34th number in turn
5. There is a column of numbers as follows: 1,4 / 5,7 / 9,10 / 13,13 / 17,16 / 21. What is the 50th? What is the 100th?
6. 2,4 / 3,6 / 7,8 / 13,10 / 21,..., then what is the nth number? (expressed by an algebraic expression containing n) Such as the title
7. 3 is a factor, 18 is a multiple. Is it right or wrong
8. Is the greatest common divisor the greatest common divisor?
9. What is the great common factor of 5 and 7
10. To know that the greatest common factor of two numbers is 21 and the least common multiple is 123, how much is the sum of the two numbers? Wrong. The least common multiple is 126
11. 2 + 22 + 222 + 2222 + 22222 + -- + 2222, please use a simple method to calculate
12. 2+22+222+2222+…… +What is 2222?
13. [high school sequence] do you know that three consecutive terms can be used to find the general formula of the sequence In the stem of the question, I only said that this is a sequence of positive numbers, and I also gave a formula. The first question is to find a1a2a3, and the second question is to find the general term formula. I derived A1, A2, A3. Can I use a3-a2 = a2-a1 = D or A3 / A2 = A2 / A1 = q to find the general term formula? Or should I use the formula given by the stem of the question to prove it? Although I have made the correct answer in both methods. The question is a little long. No point. Who will answer, It is known that {an} is a sequence of positive numbers, and the median of the equal difference between an and 2 is equal to the median of the equal ratio between Sn and 2. I calculate A1 = 2, A2 = 6, A3 = 10, Then the second question can be directly explained as arithmetic sequence according to a3-a2 = a2-a1 = D? How to answer the questions in the exam? I feel too confused and want to close this question
14. How to calculate 2 + 22 + 222 +. 2222?
15. What are the rules of the results of 2 * 22 * 22 222 * 222 2222 * 2222 22222 * 22222
16. The law of sequence 1,4,13,40121 ·
17. Sequence: 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, 19, 20 Is there a general term formula? If so, what is it? No 18. I have the wrong number. I'm sorry What is the value of the number 2013?
18. The first five terms of known sequence are 1 / 2, 5 / 4, 7 / 8, 17 / 16, 31 / 32, and its general formula is?
19. Find the general formula of the following sequence 1,0,1 / 3,0,1 / 5,0,1 / 7,0
20. “1,2,3,5,8,13,21,34,55,89,134……” This seems to be an interesting bepoche sequence in mathematics. The most important feature of this sequence is: --