How to calculate the mathematical dislocation subtraction method?

That's how it works.

sn =c1+c2+c3+c4+。。cn

1*2^2+2*2^3+3*2^4+4*2^5+..n*2^(n+1) (1)

2sn= 1*2^3+2*2^4+3*2^5+4*2^6+..n-1)*2^(n+1) +n*2^(n+2) (2)

Obtained from (1)-(2).

sn =2^2+2^3+2^4+2^5+。。2^(n+1) -n*2^(n+2)

2^(n+2)-4 -n*2^(n+2)

n-1)*2^(n+2)-4

sn =(n-1)*2^(n+2)+4

Misalignment subtraction is suitable for each item with a proportional difference. This can be done by multiplying by the proportional terms, or by dividing by the proportional terms, and subtracting them.

There is also another way to subtract the dislocation.

sn =c1+c2+c3+c4+。。cn

1*2^2+2*2^3+3*2^4+4*2^5+..n-1)*2^n +n*2^(n+1) (3)

sn/2= 1*2^1+2*2^2+3*2^3+4*2^4+..n*2^n (4)

Obtained by subtracting (4) from (3).

sn/2 = -2^1-2^2 -2^3 -2^4...2^n +n*2^(n+1)

2^(n+1)+2+n*2^(n+1)

n-1)*2^(n+1)+2

sn =(n-1)*2^(n+2)+4

The formula for the dislocation subtraction method is: a=bc, where b is the equal difference series, the general formula is b=b+n-1*d, c is the proportional series, and the general term formula is c=c*q.

Dislocation subtraction is a commonly used method of summation of sequences, which is applied to the form of multiplying proportional sequences with equations of difference. The shape is an=bncn, where bn is the equal difference series, and cn is the proportional series; List the SN separately, and then multiply all the formulas by the common ratio of the proportional series, i.e., ksn; Then make a mistake and subtract the two formulas.

The meaning of the dislocation subtraction sequence: "Dislocation subtraction" is a method of finding the sum of the number series such as potato sail, not a formula. It is mainly used to find the sum of the first n terms of the proportional series and the sum of the first n terms of the form (also informally called the difference ratio series), where, .

Rotational subtraction is that two positive integers are arbitrarily given; Determine if they are all even numbers, and if so, use 2 to reduce them; Subtract the smaller number with the larger number, then compare the resulting difference with the smaller high number, and subtract the number with the larger number, and continue this operation until the resulting minus and difference are equal, then this equal number is the greatest common divisor required. There is also a method called tossing and dividing.

For example, an=bncn, where is a series of equal differences, and the general formula is bn=b1+(n-1)*d; is an equal proportional series, and the general term formula is cn=c1*q (n-1); To sum the sequence an, first list sn, then multiply all the equations by the common ratio q of the proportional series q, that is, q·sn, and then stagger one digit to simplify the summation of the sequence an. This method of summing the sequence is called dislocation subtraction.

A brief analysis, the song is detailed and forgiving, as shown in the picture of the wild judgment.

The universal formula for dislocation subtraction is bn=b1+(n-1) d.

If the terms of a series are composed of the product of the corresponding terms of a series of equal differences and a series of proportional terms, then the first orange rough peel n terms and sn of the series can be summed by this method.

Dislocation subtraction is a commonly used method for summation of the number series, which is applied to the form of multiplying the proportional series and the equal difference series, such as an=bncn, where the equal difference series, and the general term formula is stool panicle bn=b1+(n-1) d; is an equal proportional series, and the general term formula is cn=c1*q (n-1); To sum the sequence an, first list sn, denoted as Eq:

1) Multiply all formulas by the common ratio q of the proportional sequence at the same time, i.e., q·sn, as Eq. (2), and then stagger one place to isolate Eq. (1) with Eq.

2) Make a difference, so as to simplify the summation of the number series an, this method of summation of the number circle difference series is called dislocation subtraction method.

Misplaced subtractionExamples:

Sum sn=1+3x+5x2+7x3+....+2n-1)·xn-1（x≠0，n∈n*）。

When x=1, sn=1+3+5+....+2n-1)=n2。

When x≠1, sn=1+3x+5x2+7x3+....+2n-1)xn-1。

xsn=x+3x2+5x3+7x4+…+2n-1)xn。

Subtract the two formulas to obtain (1-x)sn=1+2(x+x2+x3+x4+....+xn-1)-(2n-1)xn。

The method of complement subtraction is a method used in mathematics to solve subtraction. It is also known as the law of omnipotence, the law of complements, or the law of complement of differences. Its principle is to simplify the calculation by using the concept of complements in subtraction, converting subtraction into addition.

The universal formula for the dislocation subtraction nuclear calendar is as follows:

a - b = a + b)

where a and b are the two numbers to be subtracted, and -b is the opposite of b. This formula means that subtraction can be converted into an additive operation, where the opposite of the subtraction is added to the subtracted number to get the difference.

For example, when calculating 8 - 3, you can use the Alter Rise Misalignment Subtraction method:

Here, -3 is the opposite of 3, so subtraction can be converted to addition, adding -3 to 8 to get 5.

This misplaced subtraction simplifies subtraction operations and is suitable for subtraction of integers and rational numbers. In calculators or electronics**, the concept of complements is often used to implement subtraction operations.

Dislocation subtraction is a method of summing sequences. In the type of problem: Generally, it can only be used when the coefficient before a and the exponent of a are equal.

For example, an=bncn, where is a series of equal differences, and the general formula is bn=b1+(n-1)*d; is an equal proportional series, and the general term formula is cn=c1*q (n-1); To sum the sequence an, first list the sn, denoted as Eq. (1);

Then multiply all formulas by the common ratio q of the proportional series at the same time, that is, q·sn, which is recorded as equation (2); Then stagger one digit and make the difference between Eq. (1) and Eq. (2), thus simplifying the summation of the logarithm series an. This method of summing the sequence is called dislocation subtraction.

Classic] dislocation subtraction is a method used to calculate the sum of successive integers. Its formula is: s = n 2) *a + b), where s is the sum, n is the number of consecutive integers, a is the first term, and b is the last term.

This formula can be explained by geometric methods. Suppose we have a series of consecutive integers, from a to b. We can arrange these integers into a series of equal differences, where the difference between two adjacent numbers is 1.

In this way, we can divide this series of equal differences into two parts: from a to b-1 and from a+1 to b.

Now, we notice that the sum of each logarithm in these two parts is the same. For example, the sum of a + b-1) is equal to the sum of (a+1) +b. This is because they are both equal to A + B.

Based on this observation, we can divide the whole sequence of equal differences into n 2 logarithms, and the sum of each pair is equal to a + b. Therefore, the sum s is equal to n2 multiplied by the sum of each log.

Since the sum of each logarithm is a + b, we can simplify the formula to: s = n 2) *a + b).

Therefore, the formula for dislocation subtraction is based on the properties of a series of equal differences, and the sum of the chaotic branches is obtained by dividing successive integers into pairs and calculating the sum of each pair.