# Ha HaHa HaHaHa!

**Number Theory**Level 3

\[\huge 5,\quad 55,\quad 555,\quad 5555,\quad ...\] If general term of this sequence is \(\dfrac{A}{B}(C^{n}-D)\) where A,B,C,D are positive integers, \(n=1,2,3,4,...\) , and \(\dfrac{A}{B}\) is an irreducible fraction. Find the value of \(\dfrac{C!-B!}{(A+D)!}\)