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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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