The general term of some series can be expressed by two or more formulas. There is also a series with general formula, such as a series composed of all prime numbers. Sequence can also be regarded as a function whose domain is natural number set n (or its finite subset {1, 2,3, n}), and the list of corresponding function values when the independent variable values are from small to large.
Find the relevant interpretation of the law:
In fact, it is to strengthen the understanding of the general law of sequence. Although it has many solutions, it is mainly to cultivate the ability to discover the general law of series and guess the general term of series (that is, the ability to use incomplete induction), so that when we encounter some series that are difficult to find the general term by general methods, we can guess the general term formula of this series quickly and accurately through the first few terms.
Then prove it by mathematical induction or reduction to absurdity or other methods, bypass the front mountain and get its general formula quickly. Therefore, finding the rules to fill in the blanks will still help us to enhance our understanding of some difficulties and characteristic series. There are countless search patterns, some of which are regular between given numbers and some are regular between every other number. In addition, the difference between two adjacent numbers shows a certain law, which may be the same addition, the same subtraction, the multiplication of the same number or series, or the square.