Chapter 13 - Sequences and Series - 13.3 Finite Geometric Series - Exercises and Problems for Section 13.3 - Exercises and Problems - Page 552: 5

$ 781.248$

The sum of the finite geometric series can be computed as: $S_n=\dfrac{a_1(1-r^n)}{1-r}$ We have: $a_1=\dfrac{1}{25}$ and $r=5$ and $n=4-(-4)=8$ Therefore, $S_8=\dfrac{\dfrac{1}{25}(1-5^8)}{1-5}=\dfrac{1}{(125)(4)}(5^8-1) = 781.248$