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

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