If the sum of the first n terms of the sequence an is Sn, then Sn =?
∵ the general term a [n] = n ^ 2 [(Cosn π / 3) ^ 2 - (Sinn π / 3) ^ 2], the sum of the first n terms is s [n] ∵ a [n] = n ^ 2cos (2n π / 3) ∵ s [n] = 1 ^ 2 (- 1 / 2) + 2 ^ 2 (- 1 / 2) + 3 ^ 2 + 4 ^ 2 (- 1 / 2) + 5 ^ 2 (- 1 / 2) + 6 ^ 2 +... + n ^ 2cos (2n π / 3) when n = 3K-2, that is: k = (n + 2) / 3: s [3K-2] = (- 1 / 2) = (- 1 / 2)
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- 1. 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 =?
- 2. 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
- 3. Given the first n terms of sequence {an} and Sn = n ^ 2 + N + 1, is an arithmetic sequence?
- 4. 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
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- 6. 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 =?
- 7. What is the sum of split term subtraction, dislocation subtraction, reverse order addition and reverse order addition?
- 8. Which mathematician put forward these ideas first
- 9. When and which method should be used?
- 10. 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!
- 11. If the sum of the first n terms of the sequence an is Sn, then S30 =?
- 12. 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?
- 13. 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?
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- 15. Let the first n terms of sequence {an} and Sn = N2, then A8=______ .
- 16. The general term formula of sequence {an} is an = ncosn π 2 + 1, the sum of the first n terms is Sn, then s2012=______ .
- 17. 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 =
- 18. 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
- 19. We know the arithmetic sequence {an} A1 = 25, S17 = S9; The known arithmetic sequence {an} A1 = 25, S17 = S9 \X05 (1) the general formula of {an}; \x05(2)S1、S2、… Which one is the largest? And find the maximum
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