Dislocation subtraction is a method of solving problems by summation of series. In the question type: generally, it can only be used when the coefficient before a is equal to the index of a. The form is An=BnCn, where {Bn} is arithmetic progression and the general formula is bn = b1+(n-1) * d; {Cn} is a geometric series, and the general formula is cn = c1* q (n-1); Sum the sequence An, first list Sn, and record it as formula (1);

Then multiply all formulas by the common ratio q of geometric series at the same time, that is, q Sn, and record it as formula (2); Then stagger one bit, and make the difference between equation (1) and equation (2), thus simplifying the summation of the sequence an. This method of summation of series is called dislocation subtraction.

Extended data

The sum of series sums the numbers arranged according to a certain law. Finding Sn is essentially a general formula for finding {Sn}, so we should pay attention to understanding its meaning. Common methods include formula method, dislocation subtraction method, anti-addition method, grouping method, split term method, mathematical induction method, general term reduction method and union term summation method. Sequence is an important content of algebra in senior high school, and it is also the basis of learning advanced mathematics.

It plays an important role in college entrance examination and various math competitions. Sum of series is one of the important contents of series. Except arithmetic progression and geometric progression have summation formulas, the summation of most series requires certain skills.

Baidu encyclopedia-dislocation subtraction

Baidu Encyclopedia-Sum of Series