Mathematical problems of senior two about sequence of numbers It is known that the unequal positive numbers A1, A2,... An form an equal ratio sequence, and AI ≠ 1, (I = 1,2,..., n) Prove: 1 / lga1 times lga2 + 1 / lga2 times lga3 +... + 1 / lgan-1 times lgan = n-1 / lga1 times lgan
Let the common ratio be q.1/lga1ga2 = (1 / lga1-1 / lga2) / lgq, so the original formula = lgq (1 / lga1-1 / lga2 + 1 / lga2. + 1 / lgan) = lgq (1 / lga1 + 1 / lgan) = n-1 / lga1gan
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- 1. Thank you for your answer^~ 1. Given the tolerance D ≠ 0 of the arithmetic sequence {an}, and A1, A3 and A9 are equal proportion sequence, then (a1 + a3 + A9) / (A2 + A4 + A10) =? 2. In the sequence {an}, an + 1 (n + 1 is the angle sign) = an ^ 2 / (2an-5). If the sequence is both equal difference sequence and equal ratio sequence, the general formula of the sequence is______ 3. Given that f (x) = 3x / (x + 3), the sequence {an} satisfies an = f (an-1) (n-1 is a diagonal) (n ≥ 2, n ∈ n *, an ≠ 0), is the sequence {1 / an} equal difference? If so, please prove it and find out its tolerance; if not, please explain the reason 4. Given the distance from the image vertex of the quadratic function f (x) x ^ 2-2 (10-3n) x + 9N ^ 2-61n + 100 (n ∈ n *) to the y-axis to form the sequence {an}, find the general formula of (1) sequence {an} (2) The first n terms and s of sequence {an}
- 2. Mathematical sequence problems in Senior Two A unicellular animal reproduces in half and splits every two minutes. Suppose one such cell is placed in a container containing nutrient solution for exactly one hour. If two such cells are placed in the container at the beginning, it will take minutes to fill the container To solve the inequality (2x-6) / (2x ^ 2-5x + 2) ≤ 3, let's look at this problem again, although it is not a sequence
- 3. In the arithmetic sequence {an}, A5 = 10. A12 = 31, find the general term formula an, the first 10 terms and S10
- 4. Arithmetic sequence - 2, - 4, - 6 What is the general term formula of
- 5. Given A1 = 1, an + 1 = an + 2n, finding an is known from the recurrence formula: a2-a1 = 2, a3-a2 = 22, a4-a3 = 23 An-an-1 = 2N-1 add the above n-1 to get an = a1 + 2 + 2x2 + 2x3 + 2x4 + +2(n-1)=1+2+2X2+2X3+… +2(n-1)=2(n-1) Why an = a1 + 2 + 2x2 + 2x3 + 2x4 + +2(n-1)=1+2+2X2+2X3+… +2 (n-1) = 2 (n-1)? Just like a1 + A2 + a3 + A4 +. An is equal to an in the end? (when D and A1 are all greater than zero!) And I want to know the specific steps and process of formula addition
- 6. Given that the sequence {an} satisfies an + 1 = an + 2n + 1, the general term formula of the sequence {an} can be obtained by cumulative addition Note: N and N + 1 next to a are subscripts
- 7. It is known that a (n + 1) - 2An = 3 * 2 ^ (n-1) Find an
- 8. Given the recurrence formula F (n) = (n-1) (n-2) [f (n-2) + F (n-3) + (n-3) * f (n-4)] (n > 4), find the general term formula f(n)=(n-1)(n-2)[f(n-2)+f(n-3)+(n-3)*f(n-4)] (n>4) f(1)=f(2)=2 f(3)=2 f(4)=6 f(1)=f(2)=0 There's a wrong number on it This f (n) has a multiple relation with / E when n approaches infinity Give several f (n) to facilitate the test results f(5)=24 f(6)=160 f(7)=1140 f(8)=8988 The recursion above is equivalent to the recursion below f[n]=(n-1)(f[n-1]+(n-2)*f[n-3])
- 9. Why do we need to verify n = 1 when we use the undetermined coefficient method to find the general term formula
- 10. A series of problems to solve.. eigenvalue equation, I do not understand, in self-study A (n + 1) - 5An + 6A (n-1) = 0 A1 = 1 A2 = 1 to find the general term formula of sequence
- 11. If the positive number k is the median of the real numbers 2a and 2B, and the root K is the median of a and B, then the value range of K is?
- 12. Ask for a mathematical sequence problem in Senior Two The first n terms of sequence an and Sn = 32n-n ^ 2 1. The general formula of an 2. Find the first n terms and TN of an (the first two are absolute values.)
- 13. It is known that △ ABC is an equilateral triangle, EA and CD are perpendicular to plane ABC, e and D are on the same side of plane ABC, and EA = AB = 2A, DC = a, f is the midpoint of be The verification: (1) DF ‖ plane ABC (2) AF ⊥ plane EDB
- 14. Δ ABC is a regular triangle a (1,2) B (3, - 4) to find the coordinate of point C
- 15. Although the topic is very long, I only ask the first detail, In order to promote sales, an automobile sales company has adopted a more flexible payment method. On the premise that the payment for a 100000 yuan car is paid in full within one year, it can choose the following two different payment schemes to purchase a car: 1. Payment in three installments, the first payment four months after purchase, the second payment four months after purchase, and the third payment four months after purchase 2. Pay in 12 installments, the first one month after purchase, and the second one month after purchase, The monthly interest rate is 0.8%, and the monthly interest rate is calculated by compound interest. Which of the above two schemes has less total payment? A: for scheme 1, if the amount of each payment is x 10000 yuan, then after four months, the principal and interest of the first payment will be x times 1.008 ^ 80000 yuan, For scheme 2, the first time is x times 1.008 ^ 11, the principle seems to be the same as above, but why
- 16. In triangle ABC, angle ACB = 90 degrees, PA ⊥ plane ABC, PA = 2, ab = 4, AC = 2 √ 3 Find: 1. The size of dihedral angle p-ac-b 2. The size of dihedral angle a-bc-p If drawing is not convenient, just write the letters of line and face clearly
- 17. A high school mathematics problem, elliptic, master to! Ellipse x ^ 2 / A ^ 2, y ^ 2 / b ^ 2 = 1 (a > B > 0), the straight line passing through the left focus f intersects ellipse at two points a and B, the inclination angle of straight line L is 60 °, vector AF = 2, vector FB 1. Calculate the eccentricity of ellipse 2. If AB length is 15 / 4, find the equation of ellipse C
- 18. It's very simple, but I can't do it 1. The straight line y = kx-2 and ellipse (x square) + 4 (y Square) = 80 intersect at two different points P and Q. if the abscissa of the midpoint of PQ is 2, then the chord length PQ is equal to_____ 2. P is the point on the ellipse (xsquare) / 12 + (ysquare) / 3 = 1, F1 and F2 are the two focal points. If the angle f1pf2 = 60 °, the area of the triangle f1pf2 is___
- 19. Ask the known derivative formula: y = C "C is a constant" its derivative function y '= 0, find the derivative function of y = 2x!
- 20. The center of hyperbola C is at the origin, the right focus is f (2 √ 3 / 3,0), and the asymptotic equation is y = ± √ 3x (1) find the equation of hyperbola C (2) let the line L: y = KX + 1 intersect the hyperbola C at two points a and B, and ask: when the value of K is, the circle with diameter AB crosses the focus