In the equal ratio series {an}, the role of the metric ratio plays an important role. Under the premise of clarifying the definition of the metric ratio, it is more necessary to pay attention to the implicit conditions of the metric ratio, only in this way can we solve the problem of the equal ratio series, be foolproof and accurate.
(1) Metric ratio q≠0 is the primary condition for determining metric ratio;
(2) The common ratio q≠1 is a summation formula using an equal ratio series
prerequisites;
(3) The metric ratio q≠-1 is a relatively hidden condition;
1. Sum
This solution mistakenly holds that the sequences a, a^2, a^3, ... a^n are equal ratio series with the first term a and the common ratio a. In fact, when a = 0, this sequence is not an equal ratio series. Therefore, the summation formula of the equal proportional series cannot be directly applied when solving this problem, and the correct solution to this problem is:
2. Let the sum of the first n terms of the equal ratio series {an} be Sn, and try to determine whether Sm, S2m-Sm, S3m-S2m is an equal ratio series?
This solution ignores the special case of q=-1 , when m is even , Sm = 0 , so S2m-Sm , S3m-S2m - S2m - S2m is not equal to the number series.
Sequences 1,3a,5a^2,7a^3,···,(2n-1)a^(n-1),··· The first n items and Sn.