![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Given that an = 32n − 11 (n ∈ n *), the sum of the first n terms of the sequence {an} is Sn, then the minimum value of n with Sn > 0 is () A. 10B. 11C. 12D. 13
From an = 32n − 11 (n ∈ n *), a1 + A10 = A2 + A9 = =A5 + A6 = 0, a11 > 0, S9 < 0, S10 = 0, S11 > 0, so that the minimum value of n with Sn > 0 is 11
Given the sequence {an}, if 1 / A1A2 + 1 / a2a3 + +1 / anan-1 = n / Anan + 1, prove {an} is arithmetic sequence
On the basis of the original formula, write another equation with the same structure until an + 2. Subtract the original formula to get: 1 / (an + 1) an = n + 1 / (an + 1) (an + 2) - N / Anan + 1 We assume that the tolerance is d. then the left side of the original formula = 1 / D (1 / A1-1 / A2...) =1/d（1/a1-1/...
Given that the sequence {an} satisfies A1 = 1, an + 1 = an / 1 + 2An (n belongs to n *), if A1A2 + a2a3 + +Anan + 1 ＞ 16 / 33
The known sequence {an} satisfies A1 = 1, an + 1 = an / 1 + aan (n belongs to n *)
Ask if A1A2 + a2a3 + +Ana (n + 1) > 16 / 33, find the value range of n
An + 1 = an / 1 + 2An
1/an+1-1/an=2
1/an=1+(n+1)*2=2n+3
an=1/[2n+3]
a1a2+a2a3+…… +anan+1=1/2[1/a1-1/a2+1/a2-a/a3+…… -1/（2n+3)]=1/2-1/2（2n+3)＞16/33
n＞15
RELATED INFORMATIONS
- 1. In the arithmetic sequence an, a (n + 1) = 2n + 1, then Sn = (1 / A1A2) + (1 / a2a3) （1/a99a100）=
- 2. If an = 2n (n ∈ n *), then A1A2 + a2a3 + a3a4 + +anan+1=
- 3. Let the sequence an satisfy a1 + 3a2 + 3 & # 178; A3 + +3 ^ n-1 (an) = n / 3, find the general term formula of sequence an
- 4. Given the sequence an satisfies a1 + 3a2 + 3 & # 178; A3 +... + 3 (n-1) an = n & # 178;, find the general term formula of an Is n-1 power of 3
- 5. The sum of the first n terms of sequence 11 + 2, 11 + 2 + 3, 11 + 2 + 3 + 4, a is______ ．
- 6. Can calculus be used to solve the summation of sequence in high school mathematics Common methods for finding general term of sequence Observation, induction, formula, accumulation, accumulation and multiplication The common methods of summation are as follows Formula method splitting term summation splitting term summation dislocation subtraction Can we use the calculus method to kill all the above methods? It's really troublesome to remember the above methods
- 7. The sum of 1 / 1 × 2 + 1 / 2 × 3 +. + 1 / N (n + 1) is obtained by the split term elimination method Like the title,
- 8. When to add and what to multiply
- 9. What is cumulative multiplication? How to use it?
- 10. Sum Sn = 2 * 1 / 3 + 4 * 1 / 9 + 6 * 1 / 27 + (2n + 1 / 3 ^ n) It's two times one-third, not two times one divided by three
- 11. The sum problem of sequence an = 3 / (2n-11) n belongs to positive integer, and the sum of the first n terms of sequence {an} is Sn, so what is the minimum value of n with Sn ＞ 0 Summation of sequence An = 3 / (2n-11) n is a positive integer, and the sum of the first n terms of the sequence {an} is Sn, so what is the minimum value of n with Sn > 0?
- 12. Is 1 - 8 4 100 - 9 a sequence and why
- 13. The first four terms of known sequence are 2 / 3,3 / 4,5 / 6. Write a general term formula
- 14. （2-3×5-1）+（4-3×5-2）+… （2n-3×5-n）=______ ．
- 15. Find the first n terms and Sn of sequence 1 / 2 ^ 2 + 4,1 / 4 ^ 2 + 8,1 / 6 ^ 2 + 12.1 / (2n) ^ 2 + 4N
- 16. Problems of Taylor formula in Higher Mathematics E (- x ^ 2 / 2) = 1-x ^ 2 / 2 + 1 / 2! (- x ^ 2 / 2) ^ 2 + O (x ^ 4), why is the infinitesimal of the peyano remainder o (x ^ 4) written like this? Instead of O ((- x ^ 2 / 2) ^ 2) = O (x ^ 4 / 4), I don't understand why?
- 17. On the criterion of limit existence in Higher Mathematics Let x > 0 have a (x)
- 18. There are several ways to prove the existence of limit in higher number problem. Besides monotone bounded criterion, are there any other ways to prove the existence of limit? Thank you!
- 19. Solving problems with two important limits lim 2x+3 ( ——— ) x →∞ 2x+1
- 20. On the limit of higher numbers When x → 0, (1 + x ^ 2) ^ (1 / 3) - 1 is equivalent to (1 / 3) x ^ 2, that is, the limit of the first formula divided by the second formula when x → 0 is equal to 1. How can this be calculated? Please write down the calculation process. Thank you very much