Let the sum of the first n terms of a sequence an be Sn, the N + 1st power of A1 = 1 Na = (n + 2) Sn (n belongs to n-positive) prove that the sequence Sn / N is an equal ratio sequence and find Sn if the sequence Let the sum of the first n terms of the sequence an be SN. Given that A1 = 1, the nth + 1st power of Na = (n + 2) Sn (n belongs to n positive), prove that the sequence Sn / N is an equal ratio sequence and find SN. If the sum of the first n terms of the sequence SN is TN, find TN should be explained in detail

It is proved that: n (s (n + 1) - Sn) = (n + 2) Sn, i.e. s (n + 1) / (n + 1) = 2 * Sn / N, so the sequence Sn / N is equal ratio sequence, so Sn = n * 2 ^ (n-1), TN = 1 * 2 ^ 0 + 2 * 2 ^ 1 + 3 * 2 ^ 2 +... + n * 2 ^ (n-1), 2tn =. By subtracting, TN = (n-1) * 2 ^ n + 1 can be obtained

RELATED INFORMATIONS

1. Given the first n terms of sequence {an} and Sn = n ^ 2 + N + 1, is an arithmetic sequence?
2. Let the sum of the first n terms of the sequence an be Sn, A1 = 1, an = (Sn / N) + 2 (n-1) (n ∈ n *) and prove that the sequence an is an arithmetic sequence, Let the sum of the first n terms of a sequence an be Sn, A1 = 1, an = (Sn / N) + 2 (n-1) (n ∈ n *) 1. Prove: the sequence an is the arithmetic sequence, and write the expressions of an and Sn about n respectively 2. Is there a natural number n such that S1 + S2 / 2 + S3 / 3 + +Sn / N - (n-1) ^ 2 = 2013, if it exists, calculate the value of N, if it does not exist, please explain the reason
3. If the first n terms of an and Sn = (1 / 3) ^ Na + 1 / 6, a=
4. If the sequence {an} satisfies Sn = 3A (n + 1) + 2, n ∈ n *, A1 = 1, then the general term formula of sequence an is? (n + 1) is the subscript When n ≥ 2, an = s (n) - S (n-1) = 3A (n + 1) + 2 - 3an-2 4An=3A(n+1) A(n+1) / An = 4/3 {an} is the common ratio q = 4 / 3 =?
5. What is the sum of split term subtraction, dislocation subtraction, reverse order addition and reverse order addition?
6. Which mathematician put forward these ideas first
7. When and which method should be used?
8. Senior three a round of sequence sequence sum dislocation subtraction homework master into ah It is known that the tolerance D of the arithmetic sequence an is greater than 0, and A2 and A5 are two of the equations x ^ 2-12x + 27 = 0. The sum of the first n terms of the sequence BN is TN, and TN = 1-1 / 2bn (1) Finding {an} {BN} will find that an = 2N-1, BN = 2 / 3 * [(1 / 3) of the N-1 power] (2) Note CN = anbn, find the first n terms of {CN} and Sn Is to seek the second question of dislocation subtraction!
9. Easy to understand, I have a poor foundation, too abstruse to understand ~
10. High school mathematics sequence dislocation want to reduce
11. In the sequence {an}, if an = n (sin n π / 2 + cos n π / 2), the sum of the first n terms is Sn, then S100 =?
12. If the sum of the first n terms of the sequence an is Sn, then Sn =?
13. If the sum of the first n terms of the sequence an is Sn, then S30 =?
14. If the general term an of sequence {an} is n ^ 2 {cos ^ (n * 180) / 3-sin ^ (n * 180) / 3}, and the sum of the first n terms is Sn, then S30 is?
15. If the general term of sequence {a n} a n = n & # 178; (COS & # 178; n π / 3-sin & # 178; n π / 3), the sum of the first n terms is Sn, then S30 is?
16. The general term of sequence {an} is an = n & # 178; (COS & # 178; n π / 3-sin & # 178; n π / 3), and the sum of the first n terms is SN (1) Find SN; (2) Let BN = s (3n) / (n · 4N), find the first n terms and TN of the sequence {BN}
17. Let the first n terms of sequence {an} and Sn = N2, then A8=______ ．
18. The general term formula of sequence {an} is an = ncosn π 2 + 1, the sum of the first n terms is Sn, then s2012=______ ．
19. If the general term formula of sequence an is an = ncosn π / 2 + 1 and the sum of the first n terms is Sn, then s2012 =
20. If the general term formula of sequence {an} is an = n ^ 2cosn π and Sn is the sum of its first n terms, then (s2012) / 2013 is obtained Hurry up. It's urgent