The simplified formula of 1 + 2 + 3 + 4 + 5 + 6 +. + n

(1+N)xN÷2
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1. What is the result of 1 * 2 * 3 * 4 * 5 * (n-1) * n? Is there a formula I think so too
2. When n is 2, we get 1. When n is 3, we get 3. When n is 4, we get 6. When n is 5, we get 10
3. 1 to 100 formula
4. The formula from 1 to 100. Why (1 + 100) × (100 △ 2) be more detailed
5. How much is it from 1 to 100? What's the formula?
6. What's the fastest formula from 1 10 2 10 3 to 100
7. 1, 3, 2, 6, 4, (), (), 12 ()·····
8. 1/2=1/1*2=1/1-1/2,1/6=1/2*3=1/2-1/3,1/12=1/3*4=1/3-1/4. Calculate 1 / (X-2) (x-3) - 2 / (x-1) (x-3) + 1 / (x-1) (X-2)
9. Fill in the number according to the law. (1 point) & nbsp; & nbsp; 1, 3, 2, 6, 4______ ，______ ，12，16，…
10. 1/3+1/6+1/12+1/24+…… +1/3*2^n-1+…… = ditto
11. 1+2 +3+4+…… +The formula of n
12. Given the sequence an = [1 / a (n-1)] + 2, A1 = 2, find the general term formula of the sequence
13. Given A1 = 1, a (n + 1) / a (n) = 1 / 2 in the sequence, find the general term formula of the sequence
14. What is the sum of 1 to 100?
15. 1 to 100 = 5050, how much is 1 multiplied by 100? If there is a simple algorithm, please write it by the way (simple algorithm takes precedence) Oh, my God
16. What is the law of one plus one plus two plus one hundred? I know I said it in the previous paper, but I forgot that I couldn't find it, Why divide by two?
17. If the sum of the first n terms of a sequence an is Sn = a ^ n-1 (a ≠ 0), then what is the characteristic of the sequence? What is the sequence? And prove it It's the nth power of a minus 1 Is it possible to be an arithmetic sequence?
18. It is known that in the positive term sequence {an}, for all n ∈ n *, there is an & # 178; ≤ an-a (n + 1 holds) 1. Prove: sequence It is known that in positive term sequence {an}, for all n ∈ n *, there is an & # 178; ≤ an-a (n + 1 holds). ① prove that any term in sequence {an} is less than 1. ② explore the size of {an} and 1 / N, and prove your conclusion. (mathematical induction)
19. Given the sequence an = 1 / (3 ^ (n-1)), the sum of the first n terms is SN. It is proved that for all n ∈ n *, Sn
20. Given sequence Sn = 2An + (- 1) ^ n n is greater than one, try to prove that for any m greater than 4, 1 / A4 + 1 / A5 + 1 / A6 +. + 1 / am is less than 7 / 8 I calculate an = [2 ^ (n-1) - 2 (- 1) ^ n] / 3