When to add and what to multiply

When to add and what to multiply

Recursion relation a (n + 1) - an = f (n), find an accumulation
The recurrence relation a (n + 1) / an = f (n) is used to find the multiplication of an

A simple explanation of the subtraction of wrong terms, addition in reverse order, and accumulation multiplication of the formula for N-term sum of sequence?

Dislocation subtraction method is a common summation method of sequence, which is applied to the form of multiplication of equal ratio sequence and equal difference sequence. For example, an = bncn, where BN is equal difference sequence and cn is equal ratio sequence; SN is listed separately, and then all formulas are multiplied by the common ratio of equal ratio sequence, that is, KSN at the same time; then the two formulas are subtracted by one bit
If the sum of the two terms equidistant from the first and last terms of a sequence {an} is equal to the sum of the first and last terms, the sum of a constant sequence can be obtained by adding the sum of the two terms which are written forward and backward. This method is called reverse order addition

Finding the general term formula of sequence of numbers (cumulative multiplication)
In the known sequence {an}, A1 = 1, (2n + 1) an = (2n-3) an-1 (n ≥ 2), then the general term formula of the sequence {an}