Sums with functions

$\displaystyle \sum_{k=1}^{f(x)}g(x)$

In this equation, there is no use of $k$ , in function $g$ . Therefore

$\displaystyle \sum_{k=1}^{f(x)} g(x)= m(\underbrace{g(x) + g(x) + g(x) + \ldots + g(x)}_{f(x)\text{ terms}}; \\ \displaystyle m \in R \text{ assuming any variable m, so that even if f(x) returns a non-integer result it won't affect. Now let's ignore it}\\ \displaystyle \therefore \sum_{k=1}^{f(x)} g(x) = f(x)\times g(x)$