Dislocation subtraction is a high-frequency test site in the summation part of series, which is used by students in most cities, but the result is always uncertain. As we know, the derivation method of geometric series summation formula in the previous paragraph is "dislocation subtraction". In recent years, there are many problems related to dislocation subtraction in the college entrance examination, so we should pay special attention to them when reviewing. Because addition and subtraction are inverse operations, the twin brother of dislocation subtraction is dislocation addition.

Now I want to talk about the sum of series and the sum of dislocation subtraction. Students all know that the second question in the series is mainly about the sum of the elimination of split terms and dislocation subtraction. The elimination of the split term is related to the way of thinking, and the subtraction of the misplaced term is related to the computing power. If the students' computing ability is a little weak, this kind of problem is very time-consuming. Once a link goes wrong, this question will deduct most of the points. So I'm going to talk about a technique today. As long as you master the skills, you won't make mistakes in this kind of topic. Using dislocation subtraction, you can write the second question of the series smoothly in one minute.

In the summation of series, if the general term of series is in the form of "arithmetic progression× geometric progression", the method of summation is "dislocation subtraction". Let me give you an example:

So as long as you can see that it is a linear function × exponential function, then the summation method of this series is to sum it by dislocation subtraction.

Then let's look at the first topic first. This topic is 20 12 Zhejiang liberal arts college entrance examination. I'll solve this topic in the conventional way first. What do you think is the difficulty of his calculation? Because this is a liberal arts topic, it is not particularly difficult to calculate the cost.

As you can see, it is more difficult to calculate by conventional methods. Then let's talk about how to solve this problem perfectly with skills! First of all, let everyone remember a formula:

Here, I want to emphasize to you that the formula must be remembered correctly, otherwise, once you remember it wrong, this kind of question will be wrong!

But we should also pay attention to two points:

1, the power of the general formula must be n- 1, if not, it must be changed to n-1;

2. The power of the sum of the first n terms must be n. ..

Next, solve the problem according to the skills:

You see, we get the answer on the draft first, and then follow the normal writing process. At the penultimate step, the calculation here is very complicated (this question is liberal arts, which is relatively simple), and you can skip it directly if you are skilled. In this way, if you answer correctly, you will get full marks. If you follow the routine, once a link is miscalculated, you will not be able to solve the correct answer, and you will be deducted.

Next is the second question: this question comes from the college entrance examination question of Jiangsu volume, which is a little troublesome, so the calculation is very large. We don't talk about convention, but use our formula to solve the problem smoothly:

To solve this problem, we must remember the formula, so as to write smoothly, efficiently and accurately. There is also a very important skill: eliminating cracks, scientific scaling, as mentioned in the main course. Please leave a message or contact the teacher for more problem-solving skills.