Simple interpretation of geometric progression sum

A combinatorial proof inspired by real life event, that $1+r+r^2+\ldots+r^k=\frac{1-r^{k+1}}{1-r}$ for $r\in[0,1)$.

Proof:
A student wants to take $1$ unit of lessons, which could be divided into infinitely small amounts. To take any lesson he has to first schedule with his teacher. As a forgetful person, for every $L$ unit of lessons he takes $L(1-r)$ unit of them and misses $Lr$, which he then has to reschedule.

So, the student first schedules to have $1$ unit of lessons and misses $r$. He then (re)schedules $r$, and misses $r^2$, and so on until he schedules $r^k$ and misses $r^{k+1}$. The total amount of lessons scheduled is $1+r+r^2+\ldots+r^k$, and the total lessons taken is $1-r^{k+1}$. This proves the identity.

Q.E.D.