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\[\huge 5,\quad 55,\quad 555,\quad 5555,\quad ...\] 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 \(\dfrac{C!-B!}{(A+D)!}\)

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