Proving inequality The existing one component sequence is (1 / 10) ^ 2 + (1 / 11) ^ 2 + (1 / 12) ^ 2 + +（1/1000）^2 Try to prove that the sequence is greater than 0.099 and less than 0.111

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• 1. a. B, C belong to R+ Verification: A ^ 2 / (B + C) + B ^ 2 / (a + C) + C ^ 2 / (a + b) > = (a + B + C) / 2
• 2. Let x ^ 2 + (Y-1) ^ 2 ≤ 4, find the maximum value of (x + Y-1) / (X-Y + 3)
• 3. An inequality problem in Senior High School~~ 10. It is known that P > 0, Q > 0, the median of p q is 1 / 2, and x = P + 1 / P, y = q + 1 / Q, then the minimum value of X + y is () A．6 B．5 C．4 D．3
• 4. It is known that a, B and C are the three sides of a triangle, Verification: C / (a + b) + A / (B + C) + B / (c + a)
• 5. |x+1|≤a |x-2|≤a Above is a system of inequalities, and a is less than 0 Sorry ~ A is greater than 0! Sorry
• 6. Define a new operation with "[": for any rational number a, B has a [b = B ^ 2 + 1, for example, 7 [4-4 2+1=17. 1. Fill in the blanks: 5 [=_____ ； 2. When m is a rational number, find the value of M [, (2) Given that m and N are opposite numbers, X and y are reciprocal numbers, | a | = 1, try to find the value of a ^ 2 - (M + n) ^ 2012 + (- XY) ^ 2012 Define a new operation with "[": for any rational number a, B has a [b = B ^ 2 + 1, for example, 7 [4-4 ^ 2 + 1 = 17
• 7. 2.4 × 105 36.79 × 99 + 36.79 simple calculation
• 8. What do numbers in pairs mean?
• 9. What does number pair (3,5) mean
• 10. What are the meanings of the two numbers in the number pair?
• 11. It is known that a ＞ B ＞ C, and verified that 1a − B + 1b − C ≥ 4A − C
• 12. A proof of inequality in Senior High School Let x, y, Z satisfy x + y + Z = 1 Verification: x ^ 2 / (y + 2Z) + y ^ 2 / (Z + 2x) + Z ^ 2 / (x + 2Y) > = 1 / 3
• 13. A problem of basic inequality in Senior High School If the positive numbers x and y satisfy 2x + 3Y = 11 / x + 1 / y, the minimum value is
• 14. For any real numbers a (a ≠ 0) and B, the inequality | a + B | + | A-B | ≥ m · | a | holds. Note that the maximum value of real number m is m. (1) find the value of M; (2) solve the inequality | X-1 | + | X-2 | ≤ M
• 15. Given 1 > a > b > C > 0, we prove that (1-A) · (1-B) · (1-C) is greater than or equal to 8abc It is known that the three sides of a triangle with perimeter 1 are A.B., C
• 16. Trinomial inequality a + B + C ≥ how many a & # 178; + B & # 178; + C & # 178; greater than or equal to how many a ^ 3 + B ^ 3 + C ^ 3 ≥ how many
• 17. In triangle ABC, angle a = 3, angle B, angle a-angle C = 30 degrees, then angle a =? Angle B =? Angle c =?
• 18. As shown in the figure, in △ ABC, the vertical bisector of AB intersects at D, de = 6, BD = 62, AE ⊥ BC at e, and the length of EC is obtained
• 19. In △ ABC, a = 45 °, C = 30 ° and C = 10cm, find a, B and B
• 20. It is known that, as shown in the figure, in △ ABC, ad and AE are the bisectors of height and angle of △ ABC respectively, if ∠ B = 30 ° and ∠ C = 50 ° (1) find the degree of ∠ DAE; (2) try to write out the relationship between ∠ DAE and ∠ C - ∠ B? (no proof required)