We introduced a Finsler space $F^n$ with an approximate infinite series (${alpha},{eta}$-metric $L({alpha},{eta})={eta}sumlimits_{k=0}^r(frac{alpha}{eta})^k$, where ${alpha}<{eta}$ and investigated it with respect to Berwald space ([12]) and Douglas space ([13]). The present paper is devoted to finding the condition that is projectively at on a Finsler space $F^n$ with an approximate infinite series (${alpha},{eta}$)-metric above.