Author: Scholars, at present, the summation of differential series is a difficult content in the chapter of series. Most of their sums use dislocation subtraction, which has its very good advantage-that is, the method is direct. It is very suitable for students who are not used to beating around the bush in mathematics. Many students report that this method is computationally intensive. In fact, if you master the essentials carefully, you can completely avoid such mistakes and improve the speed. In my usual study, the author came up with several other methods, each with its own merits, and put them here for encouragement. We won't introduce dislocation subtraction here. If some students don't understand this method or make mistakes easily, please leave a message below and I will answer it in detail. One: Split Sum Method Before I moved, I wrote an article about this method. The following is described in the most concise way. (r, s are undetermined constants). Note that f(n), like in form, is the product of a linear function and an exponential function, and the exponential function part is the same as the original. Next, we can use the special value method or the undetermined coefficient method to find R and S. If the corresponding coefficients are equal, we can find R and S, and then we can solve them by the split term summation method, and this method does not need to discuss the case of n= 1. Two: another version of dislocation subtraction ①-② has the solution of Sn, because all the middle ones have been eliminated. This method is essentially dislocation subtraction. Just because dislocation subtraction itself cannot eliminate the middle, leaving a geometric series sum, and this method is to subtract the geometric series first, so that the middle can be directly eliminated. Three: derivative method This method is based on the following understanding: the sum of any differential series can ultimately be summed up as the sum of the first n terms. Here, n+ 1 is deliberately kept instead of n, just to prepare for the application of derivatives. And regard an as a power function about p, not an exponential function about n, then it can be solved by the derivative formula of function division.