Given the first term A1 = 2 / 3, an + 1 = 2An / an + 1 of sequence {an}, find the first n term and Sn of sequence {n / an}

Let a (n + 1) = 2An / (an + 1) be a (n + 1) = 2An / (an + 1) 1 / a (n + 1) = (an + 1) / (2An) = (1 / 2) (1 / an) + (1 / 2) 1 / a (n + 1) - 1 = (1 / 2) (1 / an) - (1 / 2) = (1 / 2) (1 / an - 1) [1 / a (n + 1) - 1] / (1 / an - 1) = 1 / 2, which is a fixed value. 1 / A1 - 1 = 1 / (2 / 3) - 1 = 3 / 2-1 = 1 / 2 sequence {1 / an -

RELATED INFORMATIONS

1. Let the first n terms of the sequence {an} and Sn = 2an-2 ^ n 1. Find A3, A4; 2. Prove that: {an + 1-2an} is an equal ratio sequence 3. Find the general formula of {an} [sequence problem] I hope you will give generously and have a detailed process Thank you ~ o (≥ V ≤) O~~
2. It is known that the sum of the first n terms of the sequence {an} is Sn and satisfies Sn = 2an-n, (n ∈ n *) (1) find the general term formula of the sequence {an}; (2) if BN = (2n + 1) an + 2n + 1 and the sum of the first n terms of the sequence {BN} is TN, find the minimum n value satisfying the inequality tn-22n-1 ≥ 128
3. In known sequence an, A1 = 2, the first n terms and Sn, if Sn = n ^ 2An, find an
4. Given that the first term of the arithmetic sequence A1 = 25, and S9 = S17, ask what is the value of N, and what is the maximum value of Sn?
5. In the arithmetic sequence {an}, if A1 ＜ 0, S9 = S12, then n is equal to___ The minimum value of Sn is obtained
6. In the arithmetic sequence {an}, Sn is the sum of the first n terms of {an}, A1 = 25, S17 = S9, find the maximum value of Sn
7. In the arithmetic sequence, when A1 is greater than 0.s9 = S17 and N is equal to, Sn has the maximum value/
8. In the arithmetic sequence {an}, it is known that A1 > 0, Sn is the sum of the first n terms of the sequence, if S9 > 0, S10
9. In the arithmetic sequence {an}, A1 = 22, S17 = S9, find the maximum value of Sn
10. In the arithmetic sequence {an}, A1 = 25, S9 = S17, then______ Item and maximum
11. It is known that the sum of the first n terms of the sequence {an} is Sn and satisfies Sn + n = 2An (n belongs to n *) It is proved that the sequence {an + 1} is an equal ratio sequence, and the general term formula of the sequence {an} is obtained If BN = (2n + 1) an + 2n + 1, the sum of the first n terms of the sequence {BN} is TN, the minimum value of N satisfying the inequality (tn-2) / (2n-1) > 2010 is obtained
12. Tell me the first n terms of the process arithmetic sequence an and s, S16 > 0, S17 = 0. What is the maximum value of N in SN
13. Let Sn be the sum of the first n terms of the arithmetic sequence {an}, A12 = - 8, S9 = - 9, then S16=______ ．
14. It is known that the sum of the first n terms of the arithmetic sequence {an} is Sn, S15 > 0, S16
15. In the known arithmetic sequence {an}, Sn is the sum of its first n terms. If S16 ＞ 0 and S17 ＜ 0, then the value of n is () A. 8B. 9C. 10D. 16
16. In the known arithmetic sequence {an}, Sn is the sum of the first n terms. If S16 ＞ 0 and S17 ＜ 0, then when SN is the largest, the value of n is () A. 16B. 9C. 8D. 10
17. Let {an} be an equal ratio sequence with common ratio Q (q is not equal to 1), and Sn be the sum of its first n terms, then the sum of the first terms of the sequence {1 / an} is?
18. In the known sequence {an}, when n is odd, an = 2N-1, when n is even, an = 3 ^ n, find the sum SN of the first n terms of the sequence
19. In known sequence an, an = 2N-1 (n is odd) an = 3 ^ n (n is even), find the first n terms and Sn
20. A sequence {an}, when n is odd, an = 5N + 1, when n is even, an = 2 ^ (n A sequence {an}, when n is odd, an = 5N + 1, when n is even, an = 2 ^ (n / 2), find the sum of the first n terms of the sequence