IKMC 2021 - Grades 11-12 - Set 2 - Self-study Question 23

$f(x+y)=f(x)f(y)$ and $f(1)=2$. Find $\dfrac{f(2)}{f(1)}+\dfrac{f(3)}{f(2)}+\cdots+\dfrac{f(2021)}{f(2020)}$.