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For all positive integers \(n,\) the sequence \(A_n\) is defined by the following relationship: \(A_n=\dfrac{n-1}{n!}.\) What is the sum of all the terms in the sequence from \(A_1\) through \(A_{10},\) inclusive?
(A) \(\dfrac{9!+1}{10!}\)
(B) \(\dfrac{9(9!)}{10!}\)
(C) \(\dfrac{10!-1}{10!}\)
(D) \(\dfrac{10!}{10!+1}\)
(E) \(\dfrac{10(10!)}{11!}\)
Answer: C
Source: Manhattan GMAT
(A) \(\dfrac{9!+1}{10!}\)
(B) \(\dfrac{9(9!)}{10!}\)
(C) \(\dfrac{10!-1}{10!}\)
(D) \(\dfrac{10!}{10!+1}\)
(E) \(\dfrac{10(10!)}{11!}\)
Answer: C
Source: Manhattan GMAT
