The summation formula of proportional series is: a(n+ 1)/an=q(n∈N).

1, 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. Equal ratio mean: If A, G and B are geometric series, G is called the equal ratio mean of A and B, that is, G 2 = AB (the product of two sides of an equilateral triangle is equal to the third side, and vice versa).

2. Monotonicity of geometric series: If series a(n) is geometric series, then the sum of the first n terms is S(n), and the common ratio is Q >；; When 1, n increases, Sn becomes faster, which is an increasing sequence; When 0

The concept of mathematics is as follows:

1. Mathematics is a subject that studies concepts such as quantity, structure, change, space and information. Mathematics is a universal means for human beings to strictly describe and deduce the abstract structure and mode of things, and can be applied to any problem in the real world. All mathematical objects are artificially defined in essence.

2. In this sense, mathematics belongs to formal science, not natural science. Different mathematicians and philosophers have a series of views on the exact scope and definition of mathematics. Number: Number is the most basic mathematical concept. Integer, rational number, real number and complex number are all different forms of numbers.

3. Algebra: Algebra is an important branch of mathematics, including dealing with variables, solving equations and studying functions. Geometry: Geometry is a branch of mathematics that studies the concepts of shape, size and position. Euclidean geometry and non-Euclidean geometry are important branches of geometry. Logic: Logic is a branch of mathematics that studies reasoning and proof, including formal logic and informal logic.

4. Probability statistics: Probability statistics is a branch of mathematics that studies random phenomena, data analysis and probability distribution. Discrete mathematics: Discrete mathematics is a branch of mathematics that studies discrete structures such as sets, graphs and trees. Analysis: Analysis is a branch of mathematics that studies continuous structures (such as functions and manifolds), including calculus, real analysis and complex analysis.