As $\frac1{(1-x)^2} = {1+2x+3x^2 +...nx^{n-1}} + \frac{x^n}{(1-x)^2} + \frac{nx^n}{(1-x)}$, is this is a function of only $x$ or both $x$ and $n$? $$\frac1{(1-x)^2} = {1+2x+3x^2 +...nx^{n-1}} + \frac{x^n}{(1-x)^2} + \frac{nx^n}{(1-x)}$$
Now, the LHS seems to be a function of only $x$, whereas the RHS seems to be a function of both $x$ as well as $n$. Please remove this ambiguity for me as I don't understand why is it that by simply choosing a value of $x$ on LHS is immaterial of what value $n$ holds.

If you rewrite as:
$$\lim\limits_{n\to\infty}\sum\limits_{i=1}^n ix^{i-1}$$
the '$n$' is just an index.
