upper bound of a function from M/M/k/k loss system

Consider the function

$$f(K) = frac{frac{rho^{K+1}}{(K+1)!}}{sumlimits_{i=0}^Kfrac{rho^i}{i!}}$$

where $K = 1, 2, 3, cdots$ and $rho > 0$.

Can we give a upper and lower bound (function of $K$ and $rho$) for this function?