SEAMO 2027 - Paper F - SET 04 - Self-study Question 24

Let $f(x)=(1+5x)/(5-25x)$, and let $f^n$ denote composition of $f$ with itself $n$ times. Evaluate
$$S=f(1/10)+f^2(1/10)+\cdots+f^{600}(1/10).$$