1, geometric series is a special series, whose characteristic is that the ratio of each term to its previous term is equal to the same constant. This series is widely used in mathematics, physics, engineering and other fields. The number of terms in a geometric series is infinite and can be extended to the left or right.
2. The definition of geometric series can be summarized as follows: every term in geometric series is increasing or decreasing by a constant multiple, that is, the ratio between any two terms is constant. The common ratio of geometric series is the ratio of any two terms, which is usually expressed by the letter Q. Nothing in geometric series is zero, because when one term is zero, it cannot be defined as geometric series.
3. The general formula of geometric series is: an = a 1q (n- 1), where an represents the value of the nth term, a 1 represents the value of the first term, q is the common ratio and n is the number of terms. This formula can be used to calculate the value of any item, and can also be used to judge whether a series is a geometric series.
Related knowledge of sequences
1, sequence is an important concept in mathematics, which refers to a series of numbers arranged in a certain order. Each number in the sequence has its specific position, and there are close relations and laws between adjacent numbers. Sequence has a wide range of applications in mathematics, such as algebra, geometry, probability and statistics.
2. Series can also be classified according to the characteristics of articles. For example, a constant series refers to a series in which each term is equal, a arithmetic progression refers to a series in which the difference between each term and its previous term is equal, and a geometric series refers to a series in which the ratio of each term to its previous term is equal. These special sequences have important application and theoretical research value in mathematics.
3. The research methods of sequence mainly include induction and deduction. Induction is a method to summarize the general term formula or recursive formula by observing and studying the first few terms in the sequence. The derivation rule is to deduce the values in the sequence through the known general formula or recursive formula.