f the product $\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot\frac{6}{5}\cdot\ldots\cdot\frac{a}{b}=9$, what is the sum of $a$ and $b$?
We notice that all the numerators and denominators cancel each other out except for $a$ and $b$. This leaves us with $\frac{a}{b}=9$. Therefore, $a=9b$.
To find the sum of $a$ and $b$, we substitute $a=9b$ into the equation $a+b=10b$. Since we do not have enough information to determine the exact values of $a$ and $b$, the sum can be expressed as $10b$.
Therefore, the sum of $a$ and $b$ is $\boxed{10}$.
No, try again
We see that the product simplifies to $\frac{a}{2}$, where $a$ is the numerator corresponding to the fraction $\frac{a}{2}$. Since this product simplifies to 9, we have:
\[\frac{a}{2} = 9\]
\[a = 18\].
Therefore, the sum of $a$ and $b$ is $18+2=\boxed{20}$.