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

I can write a computer program, and the result of my calculation is 304140932017133780431260816606476884437764156896051200000000 my java program import java.math .*; import java.io .* public class Test { public static void main(Stri...

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1. What is the sum of 1 to 100?
2. Given A1 = 1, a (n + 1) / a (n) = 1 / 2 in the sequence, find the general term formula of the sequence
3. Given the sequence an = [1 / a (n-1)] + 2, A1 = 2, find the general term formula of the sequence
4. 1+2 +3+4+…… +The formula of n
5. The simplified formula of 1 + 2 + 3 + 4 + 5 + 6 +. + n
6. What is the result of 1 * 2 * 3 * 4 * 5 * (n-1) * n? Is there a formula I think so too
7. 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
8. 1 to 100 formula
9. The formula from 1 to 100. Why (1 + 100) × (100 △ 2) be more detailed
10. How much is it from 1 to 100? What's the formula?
11. 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?
12. 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?
13. 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)
14. 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
15. 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
16. It is known that the sum of the first n terms of the sequence an = 1 / (3 ^ n-n-1) is SN. It is proved that Sn < 2 holds for any n ∈ n +
17. Find the sequence A1 = 1 an + 1 = (2An) / (2 + an) find the general term formula and prove it by mathematical induction
18. Mathematical induction and sequence Observe the following formula: 1=1^2 2+3+4=9=3^2 3+4+5+6+7=5^2 4+5+6+7+8+9+10=7^2 The general law provided by equation is deduced and proved by mathematical induction
19. Let {an} and {BN} which are all positive numbers satisfy the following conditions: 5 ^ an, 5 ^ BN, 5 ^ an + 1 is equal ratio sequence, lgbn, lgan + 1, lgbn + 1 is equal difference sequence, and A1 = 1, B1 = 2, A2 = 3. Guess an = n (n + 1) / 2 BN = (n + 1) * (n + 1) / 2 if we use mathematical induction, how to write when n = K + 1?
20. How to prove this series inequality by mathematical induction It is known that an + 1 (refers to the N + 1st term) = an + (an ^ 2) / (n ^ 2), A1 = 1 / 3. To prove an > 1 / 2 - 1 / 4N. In addition, I will reduce the inequality to a more strict one, and it is better to prove an > 1 / 2 - 1 / 5N first. What is the reason?