How to divide 31 into the sum of several different natural numbers, which requires the product of these natural numbers to be as large as possible?

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1. How to divide 195 into the sum of several different natural numbers, which requires the product of these natural numbers to be as large as possible?
2. Inequality expansion and contraction. Do it before tomorrow morning, add 50 points. Prove: 1 / 2n ^ 2 + 3N + 1 is less than 5 / 12, the front 2n ^ 2 + 3N + 1 is the denominator It is proved that 1 / 2n ^ 2 + 3N + 1 is less than 5 / 12 N, and 2n ^ 2 + 3N + 1 before N + is the denominator Sum.
3. It is proved by mathematical induction that when there is always 2 ^ n > n ^ 3 for a large enough natural number n, the first value no should be the minimum when the first step inequality is established
4. Prove inequality: (2-1) / (2 ^ 2-1) + (2 ^ 2-1) / (2 ^ 3-1) +. + (2 ^ n-1) / (2 ^ n + 1) - 1) > n / 2-1 / 3
5. A difficult problem of inequality, please provide some ideas to prove (2 / 1 ^ 4 + 1) (2 / 2 ^ 4 + 1) (2 / 3 ^ 4 + 1) (2/n^4+1)
6. Prove inequality 3 ^ n ≥ n ^ 3 (n ≥ 3) RT It's better not to use derivatives N is a positive integer
7. If n is a natural number, what does 2n + 1 represent? A, even number B, odd number C, prime number d, composite number
8. Divide natural number into odd number and even number according to (). How to fill in brackets
9. When n is a natural number, 2n + 1 must be odd, right?
10. If n is used to represent a natural number greater than a, then "2n - 1" must be odd
11. How to divide 30 into several different natural numbers and ask the product of these natural numbers to be as large as possible?
12. How to divide 16 into the sum of several natural numbers, which requires the product of these natural numbers to be as large as possible? My answer is 324, Montaigne,
13. What is the maximum product of dividing 16 into several natural numbers
14. Divide 16 into three natural numbers to make the product of these three numbers the largest, the largest is () Calculate by equation Urgent!
15. If 16 is divided into the sum of several natural numbers, what is the maximum product of these natural numbers?
16. Divide the natural numbers 1-200 into three groups a, B and C according to the following method: a (1, 6, 7, 12, 13, 18...) B (2, 5, 8, 11, 14, 17...) C (3,4,9,10,15,16...) how many numbers are there in each group? What is the last number in each group? Which group is 173?
17. What is the rule of the product of two adjacent natural numbers What's the rule of the product of two adjacent natural numbers?
18. If the sum of two natural numbers is 14 and their product is 48, then the two numbers are, Lie equation
19. The product of the sum of two continuous natural numbers multiplied by their difference is 99. The larger of the two natural numbers is 99______ ．
20. The product of two adjacent natural numbers is 99. What are the two numbers