First, eight elimination methods of series splitting term

Arithmetic type, irrational linear type, exponential type, logarithmic type, trigonometric function type, factorial combination number formula type, abstract type and mixed type.

1. Arithmetic type: the general term formula is in the form of arithmetic progression. After splitting the item, you can eliminate the middle arithmetic item and get the sum of the first item and the last item.

Arithmetic type is the most common form of decomposition formula, and its expression form is an2+bn+c, in which a≠0 is gradually derived according to certain laws. The n2 term can be written as the sum of arithmetic progression, then it can be written as two products, and then it can be subtracted and eliminated.

Example: Solve equation x2-3x-6=0.

Step 1: Let x2-3x-6=0, where a= 1, b=-3 and c=-6.

Step 2: Let x2-3x=6, that is, x2-3x+6-6=0, where a= 1, b=-3 and c=0.

Step 3: Write the form of two products according to the arithmetic form: (x–3) (x+2) = 0.

Step 4: X-3 = 0, x+2=0, that is, x-3=0 3, -2.

2. Irrational number line: the general formula is the form of irrational number. After splitting the term, you can eliminate the irrational number term in the middle and get the sum of rational numbers.

Irrational number line refers to the situation that irrational numbers appear in expressions (irrational numbers are numbers that cannot be expressed by the product quotient of finite integers and rational numbers). There are two forms: radical and fractional. The expression form is an2+bn+c, where a≠0. According to certain laws, an2 or bn can be written as two products, and then subtracted and eliminated.

Example: Solve equation 25x2+25x-30=0.

Step 1: Let 25x2+25x-30=0, where a=25, b=25 and c=-30.

Step 2: Let 25x2+25x=30, that is, 25x2+25x+30-30=0, where a=25, b=25 and c=0.

Step 3: Write the form of two products according to the form of irrational lines: (5x+6)(5x-5)=0.

Step 4: We can get 5x+6=0 and 5x-5=0, that is, x=-6/5 and 5/5= 1.