/sci/ - Science & Math

Helloooooo /mg/. It's a me again. I have another problem. I hope you guys like it. I haven't attempted it yet but it shouldn't be super difficult.
The book says that you should try a combinatorial proof, a generating function proof and an algebraic one.
Of course I'm not going to try to do all :DDDD Me, I'm going to try it combinatorially but you should feel free to do what you want. And just to clarify, [eqn]G_n[/eqn] means the set of all permutations [n].
I hope everything else is clear.
I appreciate anyone taking the time to attempt this. If you have any interesting things you'd like to point out about this problem, let me know! And if you want any clarification or the solutions found in the book, also let me know! Have a nice day!!!