Difference between Sequence of Functions and Multivariable Functions

Question

I already know what is a Multivariable Function, which looks like the following: $$f(x,y)=\frac{x}{x+y}$$ And I just know that a Sequence of Function looks like $$f_n(x)=\frac{x}{x+n}$$ That's confusing to me. Why not, instead, just put n inside of the parentheses $$f(x,n)=\frac{x}{x+n}$$ where $$n \in N^*$$

I wonder what's the difference between those two and can that sub _n be considered as a input variable of $f$ ?

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