3. Given the sequence $\left\{a_{n}\right\}$ satisfies $a_{1}=1, a_{n-1} a_{n}=a_{n-1}-a_{n}$, its general term formula is $(\quad)$.
A. $a_{n}=\frac{1}{n}$
B. $a_{n}=n$
C. $a_{n}=n+1$
D. $a_{n}=n-1$
3. A.

Since $a_{n-1} a_{n}=a_{n-1}-a_{n}$, dividing both sides by $a_{n-1} a_{n}$ gives $\frac{1}{a_{n}}-\frac{1}{a_{n-1}}=1$. Given $a_{1}=1$, we have $\frac{1}{a_{n}}=n$, thus $a_{n}=$ $\frac{1}{n}$.