The basic idea is to make $n$ trips, returning to the start and refueling on all but the last trip. On each trip but the last, you'll leave some fuel at a new dump. You want to know how far you can go on the last trip. To make calculations easy, we'll say that a full tank contains 1 (unit) of fuel and that amount will take you a distance of 1 (other unit) of distance.
Example 1 ($n = 1$ trip). Trivial: drive until you run out of fuel. Distance covered $D(1)=1$.
Example 2 ($n=2$). On the first trip, travel $x$ distance, so you'll have $1-x$ fuel remaining. Leave just enough fuel at dump 1 to allow you to return to the start. 234
Leaving $1-2x$ at dump 1 will do the trick. On the second trip, starting with a full tank, go to the first dump (using $x$ of your fuel), top off your tank (taking $x$ from the dump, leaving $1-3x$) and drive until you run out of fuel. To maximize the distance we'll need the dump to be empty so $1-3x=0$, so $x=1/3$. The total distance you'll cover will be $D(2)=1+1/3$.
The general case. With $n$ trips, you'll hit dump 1 $2n-1$ times, dump 2 $2n-3$ times, dump 3 $2n-5$ times, and so on. To empty the dumps on the last trip, we'll place dump 1 at a distance $1/(2n-1)$, dump 2 at a further distance $1/(2n-3)$, and so on. Then the last trip will cover $$ D(n) = 1 + \frac{1}{3}+\frac{1}{5} + \dotsm + \frac{1}{2n-1} $$ If we define the $m$-th harmonic number, $$ H_m=1 + \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5} + \dotsm + \frac{1}{m} $$ then it's well known that $H_m\approx\ln m$ and we can write our distance $$\begin{align} D(n) &= 1 + \frac{1}{3}+\frac{1}{5} + \dotsm + \frac{1}{2n-1}\ & = \left(1 + \frac{1}{2}+\frac{1}{3}+ \dotsm + \frac{1}{2n-1}\right)-\left(\frac{1}{2}+\frac{1}{4}+ \dotsm + \frac{1}{2n-2}\right)\ &=H_{2n-1}-\frac{1}{2}H_{n-1} \end{align}$$ This will take an amount of trips (and fuel) that are exponential in the desired distance. For example, to go a distance of $2$, it will take $n=8$ trips and to go a distance of $5$ will take over $2200$ trips.
This (and a variant) is known as the jeep problem and is covered in more detail here. 374