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General term formula of sequence, an = - 2 [n - (- 1 / 2) ^ n], for S10 and Sn
an= -2[n-(-1/2)^n]= -2n+(-1/2)^(n-1)sn=a1+a2+.+an= -2*1+(-1/2)^(1-1) -2*2+(-1/2)^(2-1)-.- 2n+(-1/2)^(n-1)= -2*(1+2+.+n)+(-1/2)^0 -2*2+(-1/2)^1+.+(-1/2)^(n-1)= -n(n+1)+[1-(-1/2)^n]/[1-(-1/2)]= -n(n+1)+...
RELATED INFORMATIONS
- 1. Let the arithmetic sequence {an}, A5 = - 3, S10 = - 40 (I) find the general term formula of the sequence {an}; (II) if the sequence {ABN} is an equal ratio sequence, B1 = 5, B2 = 8, find the first n terms and TN of the sequence {BN}
- 2. If an = 2 / N (n + 2), then S10 is equal to SN An = 2 divided by (n times N + 2)
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- 5. It is known that the general term formula of sequence {an} is an = 8N (4n2 − 1) 2, and Sn is the sum of the first n terms. The values of S1, S2 and S3 are calculated. According to the calculation results, the formula for calculating SN is deduced and proved by mathematical induction
- 6. It is known that the sum of the first n terms of sequence {an} is Sn = n & sup2; + 2n (1) the general term formula of sequence an (2) TN = 1 / A1A2 + 1 / a2a3 + 1 / a3a4 +... + 1 / ana
- 7. Arithmetic sequence {an} A1 = 2, d = 2, find the first n terms and Sn, and find the first n terms and TN leading to formula {1 / Sn}
- 8. Given an = N2 ^ n, find the expression of the first n terms and Sn of the sequence
- 9. If the first n terms of sequence {an} and Sn = N2 + 1, find the general term formula
- 10. Given the first n terms of the sequence {an} and Sn = N2, we can find the general term formula of the sequence
- 11. It is known that the sum of the first n terms of sequence an is Sn, and the point (an, Sn) (n ∈ n) is on the image of function y = 18-2x 1 find the formula of sequence an Let BN = lgan, try to judge whether BN is equal difference sequence or equal ratio sequence, and prove your conclusion 3 find the n value of the first n terms and the maximum value of the sequence BN in 2
- 12. Let the sum of the first n terms of the sequence {an} be Sn, and the points (n, Sn / N) (n belongs to n) are all on the graph of function y = 1 / 2x-1 / 2 Let the sum of the first n terms of the sequence {an} be Sn, and the points (n, Sn / N) (n belongs to n) are all on the image of the function y = 1 / 2x-1 / 2, (1) Find the general term formula of sequence {an};
- 13. Let Sn be the sum of the first n terms of the sequence an, and the point P (an, Sn) (n ∈ n +, n ≥ 1) be on the straight line y = 2x-2. (I) find the general term formula of the sequence an; (II) mark BN = 2 (1 − 1An), the sum of the first n terms of the sequence BN is TN, and find the minimum value of n such that TN > 2011; (III) let the positive sequence CN satisfy log2an + 1 = (CN) n + 1, and find the maximum term in the sequence CN
- 14. Given that the sequence {an}, Sn is the sum of the first n terms, and satisfies 3an = 2Sn + N, n is a positive integer, it is proved that the sequence {an + 1 / 2} is an equal ratio sequence 1. Given the sequence {an}, Sn is the sum of its first n terms, and satisfies 3an = 2Sn + N, n is a positive integer (1) And prove that the sequence {an + 1 / 2} is equal ratio sequence; (2) Note TN = S1 + S2 + S3 +. + Sn and find the expression of TN 2. It is known that the sequence {an} satisfies A1 = 1. A2 = 2, a (n + 2) = an + a (n + 1) / 2, and N is a positive integer (1) Let BN = a (n + 1) - an and prove that {BN} is an equal ratio sequence (2) Find the general expression of {an} Find the answer to the second question~
- 15. Sum of the first n terms of sequence: SN = 3an-3 ^ (n + 1) (1) prove that (a (n + 1) - 2 / 3an) is an equal ratio sequence (2) formula for finding an general term (3) compare Sn / 3 ^ n with 6N / (2n + 1) It's OK to ask the first question first,
- 16. The sum of the first n terms of the sequence an is Sn, 2Sn + 3 = 3an, (n belongs to N +). The formula for finding the general term of an
- 17. If the sum of the first n terms of the sequence {an} is Sn and 3an = 3 + 2Sn, the general term formula of an is obtained
- 18. Given that the sequence {an}, Sn is the sum of the first n terms, satisfying the relation 2Sn = 3an-3, the general term formula of {an} can be obtained
- 19. Given that the sum of the first n terms of the sequence {an} is Sn, and 2Sn = 3an-1, n *, find the general term formula of an
- 20. If 2 ^ m = a, 2 ^ n = B, 2 ^ m + N + 3 is expressed by the formula containing a and B