Methods and skills of high school mathematical sequence: formula method, reverse order addition and dislocation subtraction.

1, formula method.

If a series is arithmetic progression or geometric progression, the arithmetic difference, the first n terms of geometric progression and the formula are directly used for summation. The geometric series of concerned values is publicized as q= 1, q- 1.

2. Add in reverse order.

If the sum of the first and second "distances" of a series is equal, then the sum of the first n items of this series can be added in reverse order, for example, arithmetic progression's formula for the sum of the first n items is derived in this way.

3. Dislocation subtraction.

If the sum of a series consists of the product of the corresponding items of a arithmetic progression and a geometric progression, then the sum of the first n items of this series can be found by this method. For example, the sum formula of the first n items of geometric progression is derived by this method.

The function of sequence in mathematics;

Sequence is a special function. Its domain generally refers to a non-negative positive integer, and sometimes it can be a natural number or an infinite subset of natural numbers. Natural numbers are discrete, and sequence is usually called discrete function, which is relative to the function whose domain is real number or real number interval. As a discrete function, sequence plays an important role in mathematics.

In high school universities, except for studying mathematics, all the functions we encounter are "good functions", which are not only continuous but also derivable, such as power function, exponential function, logarithmic function and trigonometric function, and all of them are arbitrary derivatives. Sequence plays an important role in the study of these functions.