First of all, this problem is actually expanded by using the McLaughlin series of 1/( 1+x), and this expansion is unique.

Secondly, putting X forward is actually the same as leaving X in the fractional decomposition. Pay attention to the answer The only difference between the two is that the former is the n+ 1 power of x, and the latter is the n power of x ... it seems different. In fact, if you look closely, you will find that the coefficient of x to the 0 th power is 0. Everything else is the same.

Both methods are correct.