3. (11th "Hope Cup" Invitational Competition Question) If $f(x+y)=f(x) \cdot f(y)$, and $f(1)=2$, then the value of $\frac{f(2)}{f(1)}+\frac{f(4)}{f(3)}+\frac{f(6)}{f(5)}+\cdots+\frac{f(2000)}{f(1999)}$ is ( ).
A. 1999
B. 2000
C. 2001
D. 2002
3. B. Reason: From $f(x+y)=f(x) \cdot f(y)$, we know $f(k+1)=f(k) \cdot f(1)=2 f(k)$, which means $\frac{f(k+1)}{f(k)}=2$. Therefore, the original expression $=1000 \cdot 2=2000$.