For all positive integers $n,$ the sequence $A_n$ is defined by the following relationship:

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

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