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The sum of the first n terms of the arithmetic sequence {an} is Sn, and a4-a2 = 8, A3 + A5 = 26. Note TN = snn2, if there is a positive integer m, so that TN ≤ m holds for all positive integers n, then the minimum value of M is______ ．
∵ {an} is an arithmetic sequence. From a4-a2 = 8, A3 + A5 = 26, we can get Sn = 2n2-n, TN = 2-1n. If TN ≤ m is constant for all positive integers n, then we only need the maximum value of TN ≤ M. and TN = 2-1n < 2, only need 2 ≤ m, so the minimum value of M is 2. So the answer is 2
RELATED INFORMATIONS
- 1. It is known that the arithmetic sequence {an} satisfies the following conditions: A3 + A4 = 16, A4 + A5 = 20, and the sum of the first n terms of {an} is SN (I) find SN (II) finding the first n terms and TN of sequence {1 / Sn} I can do the first question,
- 2. Given that the sum of the first n terms of two arithmetic sequences {an} and {BN} is an and BN respectively, and anbn = 7n + 45N + 3, then the number of positive integers n with anbn as an integer is () A. 2B. 3C. 4D. 5
- 3. If the sum of the first n terms of two arithmetic sequences {an} and {BN} is an and BN respectively, and an / BN = 7n + 45 / N + 3, then the number of positive integers n with an / BN as an integer is? First of all, thank you
- 4. Given that the sum of the first n terms of two arithmetic sequences {an} and {BN} is an and BN respectively, and anbn = 7n + 45N + 3, then the number of positive integers n with anbn as an integer is () A. 2B. 3C. 4D. 5
- 5. Given that the sum of the first n terms of two arithmetic sequences {an} and {BN} is an and BN respectively, and anbn = 7n + 45N + 3, then the number of positive integers n with anbn as an integer is () A. 2B. 3C. 4D. 5
- 6. Given that the sum of the first n terms of two arithmetic sequences {an} and {BN} is an and BN respectively, and anbn = 7n + 45N + 3, then the number of positive integers n with anbn as an integer is () A. 2B. 3C. 4D. 5
- 7. It is known that SM and Sn respectively represent the sum of the first m terms and the first n terms of the arithmetic sequence {an}, and smsn = m2n2, then aman=______ ．
- 8. In the equal ratio sequence {an}, the sum of the first n terms is SN. If SM, SM + 2, SM + 1 are equal difference sequence, then am, am + 2, am + 1 are equal difference sequence. (1) write the inverse proposition of this proposition; (2) judge whether the inverse proposition is true? The proof is given
- 9. It is known that the fine brushwork Q of equal ratio sequence is not equal to 1, and am, an and AP are equal ratio sequence. It is proved that m, N and P are equal difference sequence
- 10. The sequence {an} is an equal ratio sequence, m, N, P are equal difference sequence, if am = 4, an = 6, then the value of AP is equal
- 11. It is known that the positive term sequence {an}, {BN} satisfies the following conditions: for any positive integer n, an, BN, a (n + 1) are equal difference sequence, BN, a (n + 1), B (n + 1) are equal ratio sequence, And A1 = 10, A2 = 15 Verification: sequence (root BN) is arithmetic sequence General formula for solving sequence {an}, {BN} Let Sn = 1 / (A1) + 1 / (A2) + 1 / (A3) +. 1 / (an) for any positive integer n, the inequality 2asn
- 12. How to extend m + n = P + Q AP + AQ = am + an to three terms in arithmetic sequence
- 13. In the arithmetic sequence, if M + n = P, then am + an = AP? In the arithmetic sequence, if M-N = P, then am an = AP?
- 14. In the arithmetic sequence, if M + n = P, then am + an = AP holds?
- 15. If M + n = P + Q + R, am + an = AP + AQ + Ar holds?
- 16. If M + n = P + Q, M N P Q ∈ n *, there is am + an = AP + AQ in the arithmetic sequence, what about in the arithmetic sequence?
- 17. In the arithmetic sequence {an}, M-N = Q-P, then am an = AQ AP
- 18. It is known that {an} is an arithmetic sequence. When m + n = P + Q, is there necessarily am + an = AP + AQ?
- 19. It is known that the sequence {an} is an equal ratio sequence, m, N, P ∈ n *, and m, N, P is an equal difference sequence
- 20. If {an} is an arithmetic sequence, it is proved that {2 ^ an} is an arithmetic sequence