For all positive integers \(n,\) the sequence \(A_n\) is defined by the following relationship:

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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