Geometric series refers to a series in which the ratio of each term to its previous term is equal to the same constant from the second term, usually expressed by G and P. This constant is called the common ratio of geometric series, usually expressed by the letter Q (q≠0), and geometric series a 1≠0. Where each item in {an} is not 0. Note: When q= 1, an is a constant series.

Commonly used geometric series formulas are:

1, general formula: an = a 1 * q (n- 1).

2. summation formula: sn = a1* (1-q n)/(1-q) (q ≠1) or sn = n * a1(q =/kloc.

Geometric series is a special series in mathematics, and its characteristic is that the ratio of each term to the previous term is equal. This series also has many applications in real life, such as finance, science, engineering and other fields will use the concept of geometric series. The definition of geometric series is: if the ratio of any two adjacent items in a series is equal to the same constant, then the series is called geometric series.

Geometric series has many important properties and formulas. First, its general term formula can be used to find the value of any term. The general formula is an = a 1 * q (n- 1), where a 1 is the first term, an is the nth term, and q is the common ratio. With this formula, we can easily calculate any term in the geometric series. The summation formula is sn = a1* (1-q n)/(1-q) (q ≠1) or Sn=n*a 1(q= 1).

In addition to these basic properties and formulas, geometric series has other important properties. For example, when the common ratio is greater than 1, the terms of geometric series will increase faster and faster; When the common ratio is less than 1, the terms of geometric series will decrease gradually. In addition, geometric series has the concepts of infinite series, convergence and divergence, which is an important content of learning geometric series. Geometric series has many applications in real life.

In the financial field, people often use compound interest calculation to make investments and loans, and compound interest calculation is based on the principle of geometric series. In the field of science, many natural phenomena can be described by geometric series, such as radioactive decay and population growth. In the engineering field, geometric series can be used to design various systems and models, such as electronic circuits and signal processing. In a word, geometric series is an important concept in mathematics.