How many squares are there in natural numbers 100 to 200?

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• 1. Natural numbers m, n satisfy m + n = 1991, prove: 10 ^ m + 10 ^ n is a multiple of 11? Who knows?
• 2. M. N is a non-zero natural number, and 1 / M-1 / N = 2 / 143, M + n = () how to do
• 3. If the natural number AB satisfies 1 / A-1 / b = 1 / 182 and a: B = 7:13, what is the sum of a + B Why is this 13 / 7b-1 / b = 1 / 182 Here is (13-7) / 7b = 1 / 182 Why (13-7) / 7b = 1 / 182 The process should be very detailed,
• 4. Compare the fractions n / M and n-a / M-A (m, N, a, are all non-zero natural numbers)
• 5. Let a and B be natural numbers and satisfy 11 / A + B / 3 = 17 / 33, then a + B = ()
• 6. Let a, B, C be real numbers, and prove: A & sup2; B & sup2; + B & sup2; C & sup2; + A & sup2; C & sup2; ≥ ABC (a + B + C)
• 7. It is proved that √ A & sup2; + B & sup2; + C & sup2; / 3 ≥ a + B + C / 3 ≥ & sup3; √ ABC (where a, B, C ∈ positive real numbers, and each pair is unequal),
• 8. Step 1: take a natural number N1 = 5, calculate the square of N1 plus 1 to get A1; step 2: calculate the sum of all numbers of A1 to get N2, calculate the square of N2 plus 1 to get A2 Three steps: calculate the sum of the numbers of A2 to get N3, and add 1 to the square of N3 to get A3
• 9. The first step: take a natural number N1 = 5, calculate N1 + 1 to get A1; the second step: calculate the sum of all numbers of A1 to get N2, and calculate the square of N2 + 1 to get A2· V step 1: take a natural number N1 = 5, calculate the square of N1 + 1 to get A1; step 2: calculate the sum of all numbers of A1 to get N2, and calculate the square of N2 + 1 to get A2· Step 3: calculate the sum of the numbers of A2 to get N3, and then calculate the square of N2 The first step: take a natural number N1 = 5, calculate the square of N1 + 1 to get A1; the second step: calculate the sum of all numbers of A1 to get N2, and calculate the square of N2 + 1 to get A2· Step 3: calculate the sum of the numbers of A2 to get N3, and then calculate the square of N2 to get A3... And so on, then A2010 =?
• 10. The first step is to take a natural number N1 = 5 and calculate the square 1 + 1 of n to get A1; the second step is to calculate the sum of the digits of A1 to get N2 and calculate the square 2 + 1 of n to get A2; Step 3: calculate the sum of the digits of A2 to get N3, and calculate the square 3 + 1 of n to get A3; '; then A2010 =?
• 11. How to calculate the sum of incomplete squares of 100 natural numbers from 1 to 100?
• 12. For the natural number n, the sum of the numbers is Sn, such as s2005 = 2 + 0 + 0 + 5 = 7, then S0 + S1 + S2004+S2005=?
• 13. The sum of all digits of natural number n is Sn, such as n = 38, Sn = 3 + 8 = 11; n = 247, Sn = 2 + 4 + 7 = 13. If n-sn = 2007 is satisfied for some natural numbers, the maximum value of n is () A. 2025B. 2023C. 2021D. 2019
• 14. Let a = {x | x = 2n + 1, n ∈ n}, B = {x | 1 ≤ x ≤ 10}, C = {x | x = 3N, n ∈ n}, find (a ∩ b) ∩ C
• 15. It is stipulated that the "H operation" of positive integer n is: ① when n is odd, H = 3N + 13; ② when n is even, H = NX1 / 2x1 / 2 Where h is odd For example, the result of number 3 after one "H operation" is 22, the result after two "H operations" is 11, and the result after three "H operations" is 46 (1) Find 257, after 257 times of "H operation" to get the result (2) If the result of "H operation" is always constant a, find the value of A I want to solve the problem
• 16. What is the answer to an h-operation with odd number 3N = 13 and even number * 1 / 2 until odd number 257?
• 17. It is stipulated that an operation on positive integer n, whose rule is: F (n) = 3N + 1 (n is odd) 2n − 1 (n is even), then f (3)=______ ，f[f（1）]=______ ．
• 18. What are the number of items and times in a ^ 3-A ^ 2b-b ^ 3, 3N ^ 4-2n ^ 2 + 1?
• 19. If the 2nth power of x = 3, find the value of the fourth power of (- 1 / 3 x to the 3nth power) / [the 2nth power of 4 (X & # 179;)]
• 20. 3 × 9 ^ n × 27 ^ n-1 = 3 x 3 ^ 2n x 3 ^ (3n-3)