The core idea of this kind of topic is to turn power series into familiar geometric series as far as possible, such as geometric series with common ratio x, the first term of 1 and so on, so that it is convenient to find its sum.

In order to achieve this goal, it is usually necessary to take the derivative (integral) one by one and then the derivative (derivative). The above operations can only be carried out within the convergence interval.

2. What are the steps?

Usually, the convergence radius and convergence interval of power series are obtained first.

If the power series has n, (n+ 1) and other coefficients, we must first integrate the series item by item. If these coefficients are omitted, it may become a geometric series, and then sum. Of course, for the corresponding integral, you must remember to take the derivative of the sum of this series in the future.

Similarly, if the power series has 1/n, 1/(n+ 1) and other coefficients, we must first derive the series item by item, in order to simplify these coefficients, turn them into geometric series, and then find their sum. Just integrate the sum of this series in the future.

In short, once the derivative is taken, the integral is required later, and vice versa. Because we can regard derivative and integral as inverse operations, the purpose of doing so is to restore series.

3. What is the most difficult place to deal with?

The most difficult thing to deal with is that sometimes it is not enough to get a derivative (or integral), so it is necessary to simplify the result again, maybe put forward a factor, and then continue to get the derivative (or integral).

4. What are the skills?

Without a specific topic, it is difficult to express the skills clearly. If you understand why you want to sum the functions with the above steps, you can say that you have mastered the skills.