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Let one of {an} and {BN} be a convergent sequence and the other a divergent sequence. It is proved that {an ± BN} is a divergent sequence We also ask whether {anbn} and {an / BN} (BN ≠ 0} must be divergent sequences
If {an + BN} converges
Because {an} also converges
For any e
All have N1, N2
If k > N1, there is | (AK + BK) - L | N2, there is | (AK) - a | N1. If the larger of N2 is | (BK - (L-A) | = | (AK + BK) - L + (ak-a) | < | (AK + BK) - L | + | (AK) - a | a = 0 or {BN} - > infinity, then it will be convergent, otherwise it will diverge
How to find this limit? [1 + 3 + 5 +... + (2n-1)] / [2 + 4 + 6 +... + 2n], n tends to be positive infinity
Is there any formula for the limit of sequence and the differential quadrature of numerator and denominator
The top and bottom are equal difference series, which are calculated by the sum of the first n terms of equal difference respectively, and then the coefficient ratio of the highest order term is calculated by division
You can also use a calculator. Well, let's see how close it is
(9N ^ 2 + n) / (2n + 5) find the limit to infinity
Divide up and down by n
=(9n+1)/(2+5/n)
If n tends to infinity, then 5 / n tends to zero
So the numerator tends to infinity and the denominator tends to 2 + 0 = 2
So fractions tend to infinity
So there is no limit
It is known that the equal ratio sequence {BN} is a common ratio Q and the sequence {an} satisfies BN = 3 ^ an. (1) it is proved that the sequence {an} is an equal difference sequence. (2) if B8 = 3 and the sequence {an}
It is known that the equal ratio sequence {BN} is a common ratio Q and the sequence {an} satisfies BN = 3 ^ an, (1) it is proved that the sequence {an} is an equal difference sequence, (2) if B8 = 3 and the first three terms of the sequence {an} are S3 = 39, find the general term of {an}, (3) under the condition of (2), find TN = | A1 | + | A2 | +... + | an|
1.bn/b(n-1)=3[an-a(n-1)]=q
So an-a (n-1) = log (3) Q
2.a2=13
a8=1
d=-2
an=17-2n
3.n8 Tn=-[a1+.an]+2[a1+.+a8
=n^2-16n+128
RELATED INFORMATIONS
- 1. An is an arithmetic sequence, an = 13 + (n-1) 2. An = log2bn. It is proved that BN is an arithmetic sequence
- 2. The known sequence an satisfies: an + 1-2an = 2 ^ n + 1, and A1 = 2 (1). It is proved that {an / 2 ^ n} is the key to find the sequence an of arithmetic sequence (2)
- 3. Let {an} be an arithmetic sequence with the first term of 3 and the tolerance of D, and {BN} be a sequence determined by BN = an + an + 1, then what are the first n terms of {BN} and Sn?
- 4. Let A1 and d be real numbers, the first term be A1, the sum of the first n terms of the arithmetic sequence {an} with tolerance d be Sn, satisfying s5s6 + 15 = 0, then the value range of D is______ ．
- 5. The first term of the infinite arithmetic sequence {an} is A1 = 93, and the tolerance D1 = - 7. The first term of the infinite arithmetic sequence {BN} is B1 = 17, and the tolerance D2 = 12, Then, how many items are there in these two sequences with equal values?
- 6. If an = BN, find n
- 7. Let the sequence {an} be an equal ratio sequence, the sum of the first n terms is Sn, and S3 = 3a3, and find the value of the common ratio Q As above
- 8. It is known that the sum of the first n terms of the equal ratio sequence {an} is Sn, A4 equals 2A3, S2 equals 6. Find the general term formula of the sequence {an}
- 9. It is known that SN is the sum of the first n terms of the equal ratio sequence {an}, and S3, S9 and S6 are equal difference sequence A .A3+A6=A9 B.A3*A6=A9 C.A3+A6=2A9 D.A3*A6=A9^2 Ask for detailed explanation
- 10. The {an} is an equal ratio sequence composed of positive numbers, Sn is the sum of the first n terms, a2a4 = 1, S3 = 7, S5 =?
- 11. Let the sequence {an} {BN} be Lim an BN = 0. If an is unbounded, then BN must be bounded. Is it correct? Why?
- 12. In the expansion of (1 + 2x) ^ n, let the sum of binomial coefficients of odd terms be the sum of the first n terms of an sequence and be Sn, then what is Liman / Sn equal to
- 13. If we know that in the expansion of (1 + ax) 6, the coefficient of X3 is equal to 160, then the real number a=______ ．
- 14. If the constant term in the expansion of binomial (1 / x-ax ^ 2) ^ 9 is - 21 / 2, then the real number a =? RT
- 15. In the expansion of binomial (2x + 6) ^ 6, what is the coefficient with x ^ 4 term
- 16. How to find the maximum or minimum term of binomial coefficient expansion It's a coefficient, not a binomial coefficient,
- 17. What is the difference between the binomial coefficient of binomial expansion and that of binomial expansion
- 18. It is known that the coefficient with X term in the expansion of F (x) = (1 + 2x) m + (1 + 4x) n (m, n ∈ n *) is 36. The minimum coefficient with x 2 term in the expansion and the value of M, n are obtained
- 19. How to find the sum of the coefficients in binomial
- 20. If the limit (1 + A + A ^ 2 +... + A ^ (n-1)) = 2 / 3, then the coefficient sum of binomial (x-2a) ^ 10 expansion is