After taking off the feet from the pedal, the front wheel of a bicycle spins 500 times during the first minute.
In the next minute, it spins $\dfrac{3}{5}$ of the number it did in the last minute and so on. This process is supposed to be infinite.
I have to evaluate the number of spins until the bicycle stops. Clearly, it's a geometric series with $a_{1}=500$ and $q=\dfrac{3}{5}$.
I know I have to evaluate the infinit sum $$S_{\infty}=\frac{a_{1}}{1-q}$$ to answer the question. But why can I assume this value is when the bicycle, in fact, stops?