Question 12
Let $f(x)=\dfrac{1+10x}{10-100x}$. Set $f^n=\underbrace{f\circ f\circ\cdots\circ f}_{n\text{ terms}}$. Find the value of
$$f\left(\frac12\right)+f^2\left(\frac12\right)+f^3\left(\frac12\right)+\cdots+f^{6000}\left(\frac12\right).$$
$$f\left(\frac12\right)+f^2\left(\frac12\right)+f^3\left(\frac12\right)+\cdots+f^{6000}\left(\frac12\right).$$