(1) geometric series: an+ 1/an = q, where n is a natural number.

(2) General formula: an = a1* q (n-1);

Generalization: an = am q (n-m);

(3) summation formula: Sn=nA 1(q= 1)

sn=[a 1( 1-q)^n]/( 1-q)

(4) nature:

(1) if m, n, p, q∈N, m+n = p+q, then am an = AP * AQ；;

(2) In geometric series, every k term is added in turn and still becomes a geometric series.

(5) "G is the proportional average of A and B" and "G 2 = AB (G ≠ 0)".

(6) In geometric series, the first term A 1 and the common ratio q are not zero.

Note: in the above formula, a n stands for the n power of a.

Arithmetic progression's summation formula

Sn=(a 1+an)n/2

Sn=na 1+n(n- 1)d/2