First of all, recursive method is a method to deduce new conclusions from known conditions. It is usually used to solve the problem of series or recursion. By establishing the relationship between the known term and the latter term, the unknown term is gradually deduced. The recursive method is characterized by gradual progress from known to unknown, and each step is derived based on the results of the previous step.
Induction is to find out the characteristics or laws of * * * by observing a series of known examples and extend them to more general situations. Induction is usually used to prove that a proposition holds true for all natural numbers or positive integers. The characteristics of induction are from special to general. Through the observation and summary of special circumstances, a general conclusion is drawn.
In addition, recursion and induction have different applications in the process of proof. Recursive method is usually used to prove the properties of sequence or to solve the general formula of sequence, and inductive method is usually used to prove the universality of mathematical theorem or formula.
Generally speaking, recursive method and inductive method have different characteristics and applications in solving problems. Recursive method gradually deduces new conclusions through known conditions, which is suitable for series or recursive problems; Inductive rules find out the same characteristics of * * by observing known examples, and extend them to more general situations, which are suitable for proving the universality of mathematical theorems or formulas.