I am working on a project regarding gravitational decay. I have a function $$f(t)=-\dfrac{64G^{3}(M_{1}M_{2})(M_{1}+M_{2})}{5c^{5}\Big(r-(f(1)+f(2)+...f(t-2)+f(t-1))\Big)^{3}}=-\dfrac{64G^{3}(M_{1}M_{2})(M_{1}+M_{2})}{5c^{5}\Big(r-\sum_{i=0}^{t-1}f(t)\Big)^{3}}$$ where $G,c,M_1,M_2$ and $r$ are set constants. When $t=1$, the sum is $0$ (This does NOT mean that the entire function for $f(1)$ is $0$!!!!).
How do I convert this into a closed form function written in terms of $G,c,M_1,M_2,$ and $r$?