What is the sum of split term subtraction, dislocation subtraction, reverse order addition and reverse order addition?

Sn=1/1*2+1/2*3+.+1/n(n+1)
=1-1 / 2 + 1 / 2-1 / 3 + 1 / 3-1 / 4 +. + 1 / (n-1) - 1 / N + 1 / n-1 / (n + 1) (cancel in the middle, only the first and last two terms are left) = 1-1 / (n + 1) dislocation subtraction, which is used in the summation formula of equal ratio sequence
Sn= 1/2+1/4+1/8+.+1/2^n
Multiply both sides by 1 / 2 at the same time
1 / 2Sn = 1 / 4 + 1 / 8 +. + 1 / 2 ^ n + 1 / 2 ^ (n + 1) (pay attention to the different positions of the original formula, so that you can write it more clearly) subtraction of two formulas 1 / 2Sn = 1 / 2-1 / 2 ^ (n + 1) Sn = 1-1 / 2 ^ n addition in reverse order. This is applied in proving the summation formula of arithmetic sequence

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3. Senior three a round of sequence sequence sum dislocation subtraction homework master into ah It is known that the tolerance D of the arithmetic sequence an is greater than 0, and A2 and A5 are two of the equations x ^ 2-12x + 27 = 0. The sum of the first n terms of the sequence BN is TN, and TN = 1-1 / 2bn (1) Finding {an} {BN} will find that an = 2N-1, BN = 2 / 3 * [(1 / 3) of the N-1 power] (2) Note CN = anbn, find the first n terms of {CN} and Sn Is to seek the second question of dislocation subtraction!
4. Easy to understand, I have a poor foundation, too abstruse to understand ~
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6. High school mathematics what kind of sequence can use superposition to find Sn, what kind of sequence can use dislocation subtraction to find Sn, it's better to be more detailed and list all the possibilities
7. It is urgent to find the sum of sequence dislocation subtraction The calculation problem is urgent
8. Using the method of dislocation subtraction to find the first n terms and the higher one sequence Given the square of. An = 4N, find the sum of the first n terms of. BN = 1 / 2-1 of an ^ 2-1
9. Examples of dislocation subtraction in sequence an=4n-2 bn=2/[4^(n-1)] cn=an/bn Finding the first n terms and TN of CN of sequence
10. How to calculate the dislocation subtraction method in the proportional sequence? I don't quite understand this algebra
11. If the sequence {an} satisfies Sn = 3A (n + 1) + 2, n ∈ n *, A1 = 1, then the general term formula of sequence an is? (n + 1) is the subscript When n ≥ 2, an = s (n) - S (n-1) = 3A (n + 1) + 2 - 3an-2 4An=3A(n+1) A(n+1) / An = 4/3 {an} is the common ratio q = 4 / 3 =?
12. If the first n terms of an and Sn = (1 / 3) ^ Na + 1 / 6, a=
13. Let the sum of the first n terms of the sequence an be Sn, A1 = 1, an = (Sn / N) + 2 (n-1) (n ∈ n *) and prove that the sequence an is an arithmetic sequence, Let the sum of the first n terms of a sequence an be Sn, A1 = 1, an = (Sn / N) + 2 (n-1) (n ∈ n *) 1. Prove: the sequence an is the arithmetic sequence, and write the expressions of an and Sn about n respectively 2. Is there a natural number n such that S1 + S2 / 2 + S3 / 3 + +Sn / N - (n-1) ^ 2 = 2013, if it exists, calculate the value of N, if it does not exist, please explain the reason
14. Given the first n terms of sequence {an} and Sn = n ^ 2 + N + 1, is an arithmetic sequence?
15. Let the sum of the first n terms of a sequence an be Sn, the N + 1st power of A1 = 1 Na = (n + 2) Sn (n belongs to n-positive) prove that the sequence Sn / N is an equal ratio sequence and find Sn if the sequence Let the sum of the first n terms of the sequence an be SN. Given that A1 = 1, the nth + 1st power of Na = (n + 2) Sn (n belongs to n positive), prove that the sequence Sn / N is an equal ratio sequence and find SN. If the sum of the first n terms of the sequence SN is TN, find TN should be explained in detail
16. In the sequence {an}, if an = n (sin n π / 2 + cos n π / 2), the sum of the first n terms is Sn, then S100 =?
17. If the sum of the first n terms of the sequence an is Sn, then Sn =?
18. If the sum of the first n terms of the sequence an is Sn, then S30 =?
19. If the general term an of sequence {an} is n ^ 2 {cos ^ (n * 180) / 3-sin ^ (n * 180) / 3}, and the sum of the first n terms is Sn, then S30 is?
20. If the general term of sequence {a n} a n = n & # 178; (COS & # 178; n π / 3-sin & # 178; n π / 3), the sum of the first n terms is Sn, then S30 is?