2. A series, if the ratio of any last term to the previous term is the same constant, that is, A(n+ 1)/A(n)=q(n∈N*), is called a geometric series, in which the constant q is called a common ratio.
Geometric series: a(n+ 1)/an=q(n∈N) General formula: an = a 1× q (n- 1) Sum formula: sn = n× a1(q =
If the proportional series converges, the absolute value of its common ratio q must be less than 1. Therefore, when n tends to infinity, the n power of q in the summation formula of proportional series tends to 0 (when | q | q is greater than 1, the proportional series diverges. Geometric series (also called geometric series): It is a special series. Its characteristic is that the ratio of each term to the previous term is a constant from the second term.