Given the general term formula of sequence {an} an = n & # 178; + N, then the first n terms of {an} and Sn =?
an =n^2+n
= n(n+1)
= (1/3)[n(n+1)(n+2) - (n-1)n(n+1)]
Sn = (1/3){ summation (i:1->n)[i(i+1)(i+2) - (i-1)i(i+1)] }
= (1/3)n(n+1)(n+2)
RELATED INFORMATIONS
- 1. 1. Given the first n terms of a sequence and Sn = n square + n-1, is it an arithmetic sequence?
- 2. 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
- 3. 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?
- 4. 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?
- 5. 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
- 6. 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?
- 7. (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
- 8. Let Sn = 2n + A and TN = n2-2n + B, then a + B=______ .
- 9. It is known that the general term formula of sequence an is an = 2N-1, and the sum of the first n terms of sequence BN is TN and satisfies TN = 1-b The general term formula of BN
- 10. Given that the general term formula of the sequence {an} is an = n / N ^ 2 + 156 (n ∈ n +), what is the maximum term of the sequence
- 11. 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
- 12. 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?
- 13. 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
- 14. Given the first n terms and Sn = 3 (3 ^ n + 1) / 2 of the sequence, find its general term formula
- 15. Given that the sum of the first n terms of sequence {an} is Sn = 2n-3, then the general term formula of sequence a is (2n, n is above)
- 16. Given the sum of the first n terms of the sequence {an} Sn = - 3 / 2n & sup2; + 205 / 2n, find the general term formula of the sequence {an}
- 17. 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
- 18. Given A1 = 1, a (n + 1) = 3an + 2 ^ (n + 1), find the general term formula of sequence {an}
- 19. A 1 = 3, a (n + 1) = 3an - 2 fast
- 20. The general term formula of sequence is 2n ^ 2-2n + 1, and the sum of the first n terms can be obtained