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Summation formula of permutation and combination
1. Equal ratio sequence
(1) Equal ratio sequence: an + 1 / an = q, n is natural number
(2) The general formula is: an = A1 * q ^ (n-1);
The generalized formula is: an = am * q ^ (n-m);
(3) Sum formula: SN = Na1 (q = 1)
Sn=[A1(1-q)^n]/(1-q)
(4) Nature:
① If m, N, P, Q ∈ N and M + n = P + Q, then am · an = AP * aq;
② In the equal ratio sequence, the sum of every k items in turn is still equal ratio sequence
(5) "G is the equal proportion of a and B", "G ^ 2 = AB (g ≠ 0)"
(6) In the equal ratio sequence, the first term A1 and the common ratio Q are not zero
Note: in the above formula, a ^ n represents the nth power of A
2. Arithmetic sequence
Sn=(a1+an)n/2
Sn=na1+n(n-1)d/2
3. Other series
There is no specific formula for these sequences, but generally they can be solved by equal ratio or equal difference sequences. In addition, there are some special solutions for some sequences, which can make the whole process very simple. These need to be summarized slowly in the learning process
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