11×3+13×5+15×7+… +12009×2011．

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• 1. Calculate 1 × 4 / 1 + 4 × 7 / 1 + 7 × 10 / 1 + 10 × 13 / 1 +... 2008 × 2010 / 1
• 2. Sin α = A-3 / A + 5, cos α = 4-2a / A + 5, find Tan (α / 2)
• 3. 2*sin(60°-B)*sinB=cos(60°-2B)-cos60°
• 4. Given Sina + SINB = 1 / 3, find the range of square 2b of sina cos! Given sin (pie-a) = 1 / 2, calculate cos (3 pie + a)
• 5. Simplification 2 / (COS ^ 2a-sin ^ 2a)
• 6. If 3sina + cosa = 0, then 1 / sin ^ 2A + cos ^ 2A = a.10/3 B.5 / 3 C.2 / 3 d. - 2
• 7. Proving trigonometric function: cos ^ 2 (a) - cos (2a) * cos (4a) = sin ^ 2 (3a) Verification: cos ^ 2 (a) - cos (2a) * cos (4a) = sin ^ 2 (3a)
• 8. If SN: TN = (7n + 1): (4N + 27), find the ratio of a11: B11
• 9. The sum of the first n terms of the sequence {an} and {BN} is denoted as an and BN respectively. It is known that an = - n-3 / 2,4bn-12an = 13N (n ∈ natural number) (base n after a, B, a, b) ① Find the analytic expression of B base n about N and the general term formula of the sequence {B base n}. ② let C base n = (1 / 2) ∧ 2B base n-3a base n, prove that {C base n} is an equal ratio sequence, and find the first n term and C base n of the sequence {C base n} (thank you for the detailed process
• 10. (2010 Susong County three modules) arithmetic {an} series of the former n items and Sn, S9=-18, S13=-52, geometric ratio {bn}, b5=a5, b7=a7, the value of B15 is () A. 64B. -64C. 128D. -128
• 11. Given that f (x) belongs to R for any x, f (- x) + F (x) = 0, f (x + 1) = f (x-1), then what is f (2011) equal to
• 12. Given K ∈ n *, let F: n * → n * satisfy: for any positive integer greater than k Given that K belongs to n *, let F: n * → n * satisfy that for any positive integer n greater than k, f (n) = n-k (1) Let k = 1, then the value of one of the functions f at n = 1 is? (2) Let k = 4, and when n ≤ 4, 2 ≤ f (n) ≤ 3, then the number of different functions f is? The problem implies that for a positive integer n less than or equal to K, its function value should also be a positive integer. I can't see how it is implied in the problem Question 2: I haven't learned the principle of step-by-step counting. Is there any other method
• 13. Given that the function f (x) defined on the positive integer set satisfies the condition: F (1) = 2F (2) = - 2F (n + 2) = f (n + 1) - f (n), then the value of F (2011) is?
• 14. About the function, just answer the fourth question
• 15. It is known that the two points of the equation 2x2-3x-5 = 0 are 5 / 2, - 1, then the image of the quadratic function y = 2x2-3x-5 and the two points of intersection of the X axis
• 16. How to get the intersection formula y = a (x-x1) (x-x2) of quadratic function
• 17. If vector AB = vector E1-E2, vector BC = vector 2e1-8e2, vector CD = vector 3E1 + 3e2, prove that a, B and C are collinear
• 18. In trapezoidal ABCD, ad is parallel to BC, angle ABC + angle c = 90 degrees, ab = 6, CD = 8, MNP is the midpoint of AD, BC and BD respectively, what is the length of Mn
• 19. Take point D in triangle ABC so that the sum of Da + DB + DC and the minimum D point is there Three companies form triangle lines in three locations of ABC, and the semi-finished products of the company come and go frequently. Therefore, we build a public warehouse location D. in order to optimize the freight of semi-finished products, we find the point d with the above conditions. We need to prove why the point D will have Da + DB + DC as the minimum
• 20. Given that the coordinates of three vertices of triangle ABC are a (0,0,2) B (4,2,0) C (2,4,0), the unit normal vector of plane ABC is obtained We just learned this, but I don't know much about it