Given the sum of the first n terms of the sequence an, Sn = an + n & # 178; - 1 (n ∈ n *) find the general term formula of the sequence an (1) (2) if BN = 1 / ana (n + 1), find the sum of the first n terms of the sequence BN
1、S(n-1)=a(n-1)+(n-1)²-1=a(n-1)+n²-2nan=Sn-S(n-1)=(an+n²-1)-【a(n-1)+n²-2n】=an-a(n-1)+2n-1a(n-1)=2n-1=2(n-1)+1∴an=2n+12、Bn=1/AnA(n+1)=1/(2n+1)(2n+3),B...
RELATED INFORMATIONS
- 1. Given that the sum of the first n terms of the sequence {an} is Sn = n & # 178; + N + 1, then the general term formula of {an} is?
- 2. Given that the sum of the first n terms of the sequence {an} is Sn = n & # 178; + n & # 189; N, find the general term formula of the sequence
- 3. Given the general term formula of sequence {an} an = n & # 178; + N, then the first n terms of {an} and Sn =?
- 4. 1. Given the first n terms of a sequence and Sn = n square + n-1, is it an arithmetic sequence?
- 5. It is known that the sum of the first n terms of the sequence is Sn = n2-3n + 1, (1) find the general term formula, (2) try to judge whether the sequence an is an arithmetic sequence
- 6. It is known that the sum of the first n terms of a sequence is Sn = N2 + 3N, and it is proved that {an} is an arithmetic sequence. What if Sn = N2 + 3N + 1?
- 7. Given the first n terms of the arithmetic sequence {an} and Sn = - 2n2-n, how to find the expression of the general term an? Sn-1 = - 2 (n-1) & # 178; - (n-1) are calculated?
- 8. Every item of sequence an is a positive number, and Sn is the sum of its first n terms. For any n which belongs to a positive integer, there is always an, Sn, an & # 178; a general formula for finding an in arithmetic sequence Let BN = an (1 / 2) 178; the sum of the first n terms of BN is TN, and prove that 1 / 2 ≤ TN ≤ 2
- 9. The first n terms of the sequence {an} and Sn = 2n & # 178; + n-1, then the general term formula of the sequence is? How is the process solved?
- 10. (1) Given that the sum of the first n terms of the sequence an is Sn, satisfying Sn = an & # 178; + BN, it is proved that an is an arithmetic sequence (2) It is known that the sum of the first n terms of the arithmetic sequence an is Sn, and it is proved that Sn / N is also an arithmetic sequence
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- 14. It is known that the sum of the first n terms of the sequence is Sn = - 3 / 2n square + 205 / 2n 1, find the general term formula, 2, find the sum of the first n terms TN
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- 17. The general term formula of sequence is 2n ^ 2-2n + 1, and the sum of the first n terms can be obtained
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