1, accumulation method.
The accumulation method is a method to solve the general term formula of the original series by constructing a new series. It obtains a new series by adding the terms of the original series in turn, which has certain regularity, so it is easy to obtain the general term formula of the original series.
2, cumulative multiplication.
Cumulative multiplication is a method to solve the general term formula of the original series by constructing a new series. It obtains a new series by multiplying the terms of the original series in turn, which has certain regularity, so that the general term formula of the original series can be easily obtained.
3. Construction method.
Construction method is a method to solve the general term formula of the original sequence by constructing a new sequence. By observing the laws of the original sequence, it constructs an auxiliary sequence related to the original sequence, which has certain regularity, so that the general term formula of the original sequence can be easily obtained.
Application of mathematical sequence;
1, Application of arithmetic progression and geometric progression in Installment Payment.
Installment payment is a common way of consumption. When buying bulk goods or services, reduce the pressure of one-time payment by installment. In the installment payment, it usually involves the application in arithmetic progression and geometric progression.
Arithmetic progression's application in installment payment is reflected in the amount to be paid each month. Generally speaking, the amount to be paid is the same every month, which is the tolerance of arithmetic progression. Through arithmetic progression's summation formula, the relationship between the total payment amount and the total payment period can be calculated.
The application of geometric series in installment payment is reflected in the interest that needs to be paid every month. Generally speaking, the interest to be paid every month is increased by a certain proportion, which is the ratio of common geometric series. The relationship between total interest and total payment periods can be calculated by the summation formula of equal ratio series.
2. The application of sequence in computer science.
There are many problems in computer science that require the knowledge of sequences. In data compression, the laws of Fibonacci series and other series are needed to realize the compression algorithm; In cryptography, some special sequences (such as Mobius inversion sequence) are needed to realize encryption and decryption algorithms; In image processing, some special sequences (such as Fourier transform) are needed to realize image transformation and processing.
3. The application of series in economic field.
In the economic field, series also has many applications. In the problem of population growth, we need to use geometric series to represent the situation of population growth; In the calculation of bank interest, arithmetic progression and geometric series are needed to express the relationship between deposit and interest. In stock price fluctuation, some special sequences (such as Brownian motion) are needed to express the randomness of price fluctuation.