What is dislocation subtraction and what is dislocation subtraction

What is dislocation subtraction and what is dislocation subtraction

It is used for multiplication of equal ratio sequence and equal difference sequence

High school mathematics series
The sine values of the three interior angles of a right angle triangle form an equal ratio sequence to find the minimum interior angle

The sine values of the three inner angles of a right triangle are in equal proportion
One angle is 90 degrees
sin90=1
Let one acute angle be x, then the other is 90-x
sinX/sin(90-X)=sin(90-X)/1
sinX=(cosX)^2=1-(sinX)^2
Let SiNx = M
be
m=1-m^2
m^2+m-1=0
Formula method for solving quadratic equation of one variable
M = (- 1 + root 5) / 2
therefore
The minimum sine value is
(- 1 + 5) / 2

The general term formula of a sequence which is neither equal ratio nor equal difference is 1 / 4N & sup2; - 1. How to calculate the sum of the first n terms of this sequence

4N & sup2; - 1 can be decomposed into
(2n+1)(2n-1)；
1 / 4N & sup2; - 1 can be decomposed into
(1/(2n-1)-1/(2n+1))/2;
So the sum of his first n terms can be
1/2(1-1/3+1/3-1/5+…… +1/(2n-1)-1/(2n+1));
Add up,
By eliminating the intermediate term, we can get the following results
(1-1/(2n+1))/2

Sequence dislocation subtraction superposition
Finding the general term an with the N-1 power of n-1 + 2 of A1 = 1 and an = a times
A 1 = 1 an = n / N + 1 * a times n-1 (n is greater than or equal to 2) to find the general term an
We have solved SN to the nth power of an = n * 2

If the title is exactly the same as that of the first floor, it is in line with the requirements of the title of the building, but the order and the last word should also be changed, it should be "sequence superposition, multiplication and dislocation subtraction": (1) a [1] = 1, a [n] = a [n-1] + 2 ^ (n-1), find the general term a [n] [sequence superposition

Sequence of several commonly used methods, such as dislocation subtraction, specific how to use, please 3Q

After multiplying by a number, it will be a number different from the previous one. At this time, the two formulas will be subtracted!

Several common methods of sequence, such as dislocation subtraction,

Multiply the left and right by the common ratio at the same time, then subtract the two expressions and simplify them

How to avoid missing items and miscalculation when using the method of dislocation subtraction to solve "equal difference divided by equal ratio sequence" or "equal difference multiplied by equal ratio"~
Miscalculation mainly occurs in the summation of the equal ratio sequence after subtraction

After the calculation, n = 1 can be brought into the test
This is what I do every time. Because of the large amount of calculation, it is impossible to do it again in the exam

Equal difference by equal ratio
CN = an * BN, an = 2 ^ n, BN = 2n, find the first n terms and TN of the sequence CN

In general, we use the dislocation subtraction: TN = C1 + C2 + C3 + C3 +... + CN, that is: TN = 2 * 2 \35;35;;; 185; + 4 * 2 ##;; 178; + 6 * 2 35353535353535353535\35\35\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\; & 8314; & 185

Who can give me a detailed talk about the specific method of offset subtraction of arithmetic sequence

For example, an = n * 2 ^ n for Sn (n is the arithmetic sequence, 2 ^ n is the arithmetic sequence, and the common ratio is 2) Sn = 1 * 2 + 2 * 2 ^ 2 + 3 * 2 ^ 3 +. + n * 2 ^ n (1) multiply both sides of the formula by the same common ratio: 2Sn = 1 * 2 ^ 2 + 2 * 2 ^ 3 +. + (n-1) 2 ^ n + n * 2 ^ (n + 1) (2) (1)_ (2)=-Sn=1*2^1+1*2^...

How to find the sum of the first n terms of the arithmetic sequence multiplied by the arithmetic sequence
For example, 1 × 2 + 2 × 4 + 3 × 8 + Of type + n * 2 ^ n

Sn=1×2＋2×4＋3×8＋…… ＋n*2^n
2*Sn=1*4+2*8+3*16+.+n*2^(n+1)
(1-2)Sn=1*2+4+8+16+.2^n-n*2^(n+1)
=2^n-2-2^(n+1)
=-2^n-2
Sn=2^n+2
Similar problems can be solved by this kind of dislocation subtraction