![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Given positive sequence {an}, the first n terms and Sn satisfy 10sn = an ^ 2 + 5An + 6, and A1, A3, A15 are equal proportion sequence, (1) find the general term of sequence {an} (the general term is an = 5n-3) (2) let BN = 2 / [an * a (n + 1)], Sn is the sum of the first n terms of sequence {BN}, find SN
Second question: because an = 5n-3,
And BN = 2 / [an * a (n + 1)],
So, BN = 2 / [(5n-3) * (5N + 2)]
Split term, BN = 2 / 5 times [1 / (5n-3) - 1 / (5N + 2)]
So Sn = 2 / 5 times [1 / 2-1 / (5N + 2)]
According to the meaning of the title, Sn
RELATED INFORMATIONS
- 1. If the first n terms of positive term sequence {an} and Sn satisfy 10sn = an ^ 2 + 5An + 6, and A1, A3, A15 are equal proportion sequence, then A2010=
- 2. Given that the sequence {an} satisfies A1 = 1, an + 1 = 2An + 1 (n ∈ n +), (1) let BN = an + 1, prove that the sequence {BN} is an equal ratio sequence; (2) find the expression of an
- 3. In the equal ratio sequence {an}, if a1 + A2 + a3 = 7, a1a2a3 = 8, and the common ratio is greater than 1, find the first sequence N and Sn of the sequence
- 4. Only the first N-term sum formula of the sequence {an} is Sn = (3) ^ n - 1, the general term formula of {an} is obtained, and it is proved that {an} is an equal ratio sequence
- 5. Given that the sum of the first n terms of the arithmetic sequence {an} is Sn = 2n & # 178; - 10N, find the values of (1) A1 and A3; (2) find A5 + A6 + A7 + A8; (3) find its general term formula and judge whether it is arithmetic sequence
- 6. Given that the sequence {an} is an arithmetic sequence, the sum of the first n terms Sn = n ^ 2, find the value of a1 + a3 + A5 + A7 +. + a25
- 7. If the tolerance of arithmetic sequence {an} d = 1 / 2, a1 + A2 + a3... + A99 = 60, calculate S100
- 8. In the arithmetic sequence {an}, d = 12, S100 = 145, then a1 + a3 + A5 + +The value of A99 is () A. 57B. 58C. 59D. 60
- 9. The tolerance of arithmetic sequence an d = 1 / 2, and S100 = 145, find a1 + a3 + A5 +. + A99 Why: M2 = A2 + A4 + A6 +... + A100 = a1 + a3 + A5 +... + A99 + (1 / 2) × 50 How does this (1 / 2) × 50 come from?
- 10. It is known that {an} is an arithmetic sequence with a tolerance of 2, and A1, A3 and A4 are proportional sequences, then the sum of the first nine terms of the sequence {an} is equal to () A. 0B. 8C. 144D. 162
- 11. Given the positive term sequence {an}, the first n terms and Sn satisfy 10sn = an2 + 5An + 6, and A1, A3, A15 are equal proportion sequence, find the general term an of the sequence {an}
- 12. Given the positive term sequence {an}, the first n terms and Sn satisfy 10sn = an2 + 5An + 6, and A1, A3, A15 are equal proportion sequence, find the general term an of the sequence {an}
- 13. Given the positive term sequence {an}, the first n terms and Sn satisfy 10sn = an2 + 5An + 6, and A1, A3, A15 are equal proportion sequence, find the general term an of the sequence {an}
- 14. In the equal ratio sequence {an}, A1 = 2, A4 = 16 are known
- 15. Given that the sequence {an} is an equal ratio sequence, a1 + a3 = 10, A4 + A6 = 5 / 4, find the value of A5 and the first n terms and S6
- 16. In the equal ratio sequence an, a1 + a3 = 10, A4 + A6 = 5 / 4, the value of common ratio q is
- 17. In the known sequence {an}, A1 = 1, an + 1 = 2An + 1, let BN = an + 1-an. (1) prove that the sequence {BN} is an equal ratio sequence; (2) let the sum of the first n terms of the sequence {Nan} be Sn, and find the minimum value of positive integer n that makes Sn + n (n + 1) 2 ＞ 120
- 18. In the arithmetic sequence {an}, A1 = 60. A17 = 12, find the sum of the first n terms of the sequence {an}
- 19. In the arithmetic sequence {an}, A1 = - 60, A17 = - 12, find the sum of the first n terms of the sequence {an} From A1 = - 69, A17 = - 12, we can get the tolerance d = 3, an = 3n-63, which can be divided into two cases, n ＞ 20 and N ≤ 20. Let Sn and s'n represent the sum of the first n terms of {an} and {an} respectively. When n ≤ 20, [I will do it], but when n ＞ 20, s'n = - S20 + (sn-s20) = sn-2s20,
- 20. If the sum of the first n terms of the arithmetic sequence {an}, {BN} is an, BN, and an / BN = n / 3n-2, then A5 / B5 =?