It is known that the equal ratio sequence {an} satisfies an > 0, n = 1, 2 When n ≥ 1, log2a1 + log2a3 + +log2a2n-1=( ) A. (n-1)2B. n2C. (n+1)2D. n2-1
∵a5•a2n-5=22n=an2,an>0,∴an=2n,∴log2a1+log2a3+… +log2a2n-1=log2(a1a3… a2n-1)=log221+3+… +(2n-1) = log22n2 = N2
RELATED INFORMATIONS
- 1. In the equal ratio sequence, Sn = 1-1 / 2 to the nth power, then a 5 is equal to what
- 2. The power of Sn = 2 in the equal ratio sequence is n + K. then what is k equal to
- 3. If the first n terms of the equal ratio sequence and Sn = 2 (13) n + K, then the value of the constant k is______ .
- 4. If the first n terms of a sequence and the formula Sn = (the nth power of 3) + B (B is a constant), is the sequence an equal ratio sequence?
- 5. Find 1 + (2 / 3) + (2 / 3) quadratic + (2 / 3) cubic + +The value of (2 / 3) n power
- 6. Cubic power of √ 3 + (- 2 √ 3) square + (√ 48 - √ 1 / √ 2 * √ 6)
- 7. If the general term formula of sequence an is an = 2n-37, what is the value of n when the first n term and Sn are minimized
- 8. If the sequence {an} satisfies A1 = 2 and an + an-1 = 2n + 2N-1, Sn is the sum of the first n terms of the sequence {an}, then log2 (s2012 + 2) is equal to () A. 2013B. 2012C. 2011D. 2010
- 9. If the sequence {an} satisfies A1 = 2 and an + an-1 = 2n + 2N-1, Sn is the sum of the first n terms of the sequence {an}, then log2 (s2012 + 2)=______ .
- 10. A sequence {an}: when n is odd, an = 5N + 1; when n is even, an = 2n2. Find the sum of the first 2m terms of the sequence (M is a positive integer)
- 11. It is known that if an is greater than 0, n = 1,2, and A5 is multiplied by 2n of a2n-5 = 2 (n is greater than or equal to 3) It is known that the equal ratio sequence {an} satisfies an > 0, n = 1,2 And a5-a2n-5 = 2 ^ 2n (n > = 3), and when n > = 1, log 2 a1+log 2 a3+… log 2 a2n-1= It is known that the sequence {an} satisfies an > 0, n = 1,2, and a (5) times a (2n-5) = 2 ^ 2n (n > = 3), log 2 a1+log 2 a3+… +log 2 a2n-1=
- 12. The results show that all items of the proportional sequence {an} are positive and A4 * A7 + A5 * A6 = 16, log2a1 + log2a2 +... + log2a10 =?
- 13. If an is an equal ratio sequence composed of positive numbers and A4 * A5 = 8, then log2a1 + log2a2 +... + log2a8=
- 14. It is known that the function f (x) = X3 + AX2 + BX + 4 is an increasing function on (- ∞, 0) and a decreasing function on (0, 1). (I) find the value of B; (II) when x ≥ 0, the curve y = f (x) is always above the straight line y = a2x-4, and find the value range of A
- 15. The monotone increasing interval of function y = | LG (x + 1) | is______ .
- 16. When the absolute values are equal, the sum is ()? When the absolute values are not equal, take the sign of () and subtract ()? When the absolute values are equal, the sum is ()? When the absolute values are not equal, take the sign of () and subtract ()?
- 17. How to find the definition field of logarithmic function Y = 1-log2 (4x-5) under the root sign
- 18. There are two numbers whose absolute value is equal to 1, right or wrong?
- 19. The function f (x) defined on R satisfies f (x + 2) = 2F (x). When x ∈ [0,2], f (x) = x2-2x, then when x ∈ [- 4, - 2], the minimum value of F (x) is___ .
- 20. Simple calculation of 15 / 0.25