We want to use as little fuel as possible so we try minimize the number of trucks we use as we go along. Let’s say we start with all 50 trucks with full fuel (5000 miles range). For each mile, we lose 50 miles in range. After two miles, we lose 100 miles leaving us with 4900 miles. This can be supported by 49 trucks so we drop one truck. As you can see for every 100 miles we lose in range, we drop a truck.
50 trucks: 100/50 49 trucks: 100/49 …
Total distance = 100/50 + 100/49 + 100/48 + … + 100/2 + 100/1 (harmonic series) = 449.920533833