The binomial series coefficient

[Aerospace93]

Homework Statement

Use the binomial series to expand the function as a power series.
1/(2+x)³

I have attached an image. I understand until the end of the second line. I don't see the reasoning used to follow through to the third line. the (-1)^n is because the sign alternates becoming negative for every odd term. Are the 2's put on the top and the bottom so then the top 2, along with the number preceding it cancel with the (n!)? I have no clue how the (n+1) comes into play.

I would appreciate all the help!

 

[CompuChip]

Yes, that is exactly the reason. The (n + 1) is there all the time, it is the number before (n + 2) :-) Only in the second line it is still absorbed in the ... dots, while in the second line it is included explicitly. I would also have included the "n" term so it is completely obvious which part cancels out against n!.